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This paper studies the problem of joint deployment, user association, channel, and resource allocation in unmanned aerial vehicle‐enabled access network. Since different user equipments performing different tasks and have different data rate requirements, the priority‐based traffic fairness problem is investigated. This problem, however, is a mixed integer nonlinear programming problem with NP‐hard complexity, making it challenging to be solved. To address this issue, a self‐organized and distributed framework "sense‐as‐you‐fly" based on the decomposition process, which divides the original problem into several subproblems, is proposed. Assuming without central controller, we derive the closed‐form resource allocation scheme and propose distributed many‐to‐one matching to optimize user association subproblem. Considering the coupled characteristics, the multi‐unmanned aerial vehicle deployment and channel allocation subproblems are modelled as a local altruistic game. The existence of Nash equilibrium is proved with the aid of exact potential game and efficient best response learning‐based algorithm is proposed. The original problem is finally addressed by solving the sub‐problems alternately and iteratively. Simulation results verify its effectiveness. By jointly optimizing multidimensional variables, the proposed algorithm unlocks network performance gains, especially in resource‐limited regimes. [ABSTRACT FROM AUTHOR]

This paper investigates the design of a model‐free adaptive iterative learning controller(MFAILC) based on sampled‐data under the presence of denial‐of‐service(DoS) attacks in nonlinear networked control systems. First, the MFAILC is presented only using I/O data, where a compensation mechanism for DoS attacks is proposed. With dynamic linearization techniques, the nonlinear system is transformed into a linear system in the iteration domain. Then an improved MFAILC is designed to actively compensate the lost data caused by DoS attacks, where the estimation of pseudo‐partial derivative (PPD) is improved by establishing the AR model. The proposed algorithm can weaken the adverse effects of the DoS attacks and ensure the excellent tracking performance of the system. Finally, the stability of the method is proved, and the effectiveness of the proposed algorithm is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

In many real‐world applications, it is important for the authors to remove insignificant image details while preserving the significant structures. This is the so‐called image smoothing problem. In this paper, the authors investigate the image smoothing problem using the lp−lq${l}_p - {l}_q$ optimization model with 0

In this paper, we study different ways for introducing memory to a parametric family of optimal two‐step iterative methods. We study the convergence and the stability, by means of real dynamics, of the methods obtained by introducing memory in order to compare them. We also perform several numerical experiments to see how the methods behave. [ABSTRACT FROM AUTHOR]

To support artificial intelligence (AI)‐involved tasks offloaded from the mobile devices (MDs), it is necessary to equip the Unmanned Aerial Vehicle (UAV) with custom‐made co‐processor (CP) for handling AI workloads in multi‐UAV‐empowered Edge Intelligence. Existing CPU‐oriented task scheduling algorithm cannot apply to the CPU+CP heterogeneous architecture. In this backdrop, this paper first formulates the joint service function placement, collaborative task scheduling, UAV deployment, and MD position determination problem as a Mixed Integer Non‐Linear Programming problem. Then, an alternating optimization‐based algorithm is put forward to derive a sub‐optimal solution of the problem utilizing Differential Evolution and Greedy‐based Hungarian algorithms. A series of experiments are conducted to evaluate the performance of the proposal. Results show that authors' proposal can achieve an overall revenue that is roughly 50% higher than those of existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the simplest quadratic matrix equation: Q(X)=X2+BX+C=0$$ \mathcal{Q}(X)={X}^2+ BX+C=0 $$. We transform this equation into an equivalent fixed‐point equation, and based on it, we construct the Krasnoselskij method. From this transformation, we can obtain iterative schemes more accurate than the successive approximation method. Moreover, under suitable conditions, we establish different results for the existence and localization of a solution for this equation with the Krasnoselskij method. Finally, we see numerically that the predictor–corrector iterative scheme, with the Krasnoselskij method as a predictor and the Newton method as corrector method, can improve the numerical application of the Newton method when approximating a solution of the quadratic matrix equation. [ABSTRACT FROM AUTHOR]

Passive millimetre‐wave (PMMW) imaging frequently suffers from blurring and low resolution due to the long wavelengths. In addition, the observed images are inevitably disturbed by noise. Traditional image deblurring methods are sensitive to image noise, even a small amount of which will greatly reduce the quality of the point spread function (PSF) estimation. In this paper, we propose a blind deblurring and denoising method via a learning deep denoising convolutional neural networks (DnCNN) denoiser prior and an adaptive ‐regularized gradient prior for passive millimetre‐wave images. First, a blind deblurring restoration model based on the DnCNN denoising prior constraint is established. Second, an adaptive ‐regularized gradient prior is incorporated into the model to estimate the latent clear image, and the PSF is estimated in the gradient domain. In a multi‐scale framework, alternate iterative denoising and deblurring are used to obtain the final PSF estimation and noise estimation. Ultimately, the final clear image is restored by non‐blind deconvolution. The experimental results show that the algorithm used in this paper not only has good detail recovery ability but is also more stable to different noise levels. The proposed method is superior to state‐of‐the‐art methods in terms of both subjective measure and visual quality. [ABSTRACT FROM AUTHOR]

Purpose: In x-ray computed tomography (CT), a violation of the Tuy data sufficiency condition leads to limited-view artifacts. In some applications, it is desirable to use data corresponding to a narrow temporal window to reconstruct images with reduced temporal-average artifacts. However, the need to reduce temporal-average artifacts in practice may result in a violation of the Tuy condition and thus undesirable limited-view artifacts. In this paper, the authors present a new iterative reconstruction method, synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON), to eliminate limited-view artifacts using data acquired within an ultranarrow temporal window that severely violates the Tuy condition. Methods: In time-resolved contrast enhanced CT acquisitions, image contrast dynamically changes during data acquisition. Each image reconstructed from data acquired in a given temporal window represents one time frame and can be denoted as an image vector. Conventionally, each individual time frame is reconstructed independently. In this paper, all image frames are grouped into a spatial-temporal image matrix and are reconstructed together. Rather than the spatial and/or temporal smoothing regularizers commonly used in iterative image reconstruction, the nuclear norm of the spatial-temporal image matrix is used in SMART-RECON to regularize the reconstruction of all image time frames. This regularizer exploits the low-dimensional structure of the spatial-temporal image matrix to mitigate limited-view artifacts when an ultranarrow temporal window is desired in some applications to reduce temporal-average artifacts. Both numerical simulations in two dimensional image slices with known ground truth and in vivo human subject data acquired in a contrast enhanced cone beam CT exam have been used to validate the proposed SMART-RECON algorithm and to demonstrate the initial performance of the algorithm. Reconstruction errors and temporal fidelity of the reconstructed images were quantified using the relative root mean square error (rRMSE) and the universal quality index (UQI) in numerical simulations. The performance of the SMART-RECON algorithm was compared with that of the prior image constrained compressed sensing (PICCS) reconstruction quantitatively in simulations and qualitatively in human subject exam. Results: In numerical simulations, the 240? short scan angular span was divided into four consecutive 60° angular subsectors. SMART-RECON enables four high temporal fidelity images without limitedview artifacts. The average rRMSE is 16% and UQIs are 0.96 and 0.95 for the two local regions of interest, respectively. In contrast, the corresponding average rRMSE and UQIs are 25%, 0.78, and 0.81, respectively, for the PICCS reconstruction. Note that only one filtered backprojection image can be reconstructed from the same data set with an average rRMSE and UQIs are 45%, 0.71, and 0.79, respectively, to benchmark reconstruction accuracies. For in vivo contrast enhanced cone beam CT data acquired from a short scan angular span of 200?, three 66? angular subsectors were used in SMART-RECON. The results demonstrated clear contrast difference in three SMART-RECON reconstructed image volumes without limited-view artifacts. In contrast, for the same angular sectors, PICCS cannot reconstruct images without limited-view artifacts and with clear contrast difference in three reconstructed image volumes. Conclusions: In time-resolved CT, the proposed SMART-RECON method provides a new method to eliminate limited-view artifacts using data acquired in an ultranarrow temporal window, which corresponds to approximately 60° angular subsectors. [ABSTRACT FROM AUTHOR]

A hybrid approach to the synthesis of sparse arrays radiating shaped or focused beampattern is presented in this paper. Specifically, an iterative scheme is used where the prescribed pattern response in the mainlobe peak direction is cast as a multi-convex problem at each step that the non-convex lower bound constraint is relaxed while including a reweighted l1-norm minimisation based on the magnitudes of the elements. Numerical tests, referred to benchmark problems, show that the proposed method achieves improved radiation performance by using fewer number of radiating elements. [ABSTRACT FROM AUTHOR]

Isomap is a well‐known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space, and b) a complete eigenvalue decomposition. Although the reduction of the computational complexity of the graphing stage has been investigated by graph processing methods, the eigenvalue decomposition stage remains a bottleneck in the problem. In this paper, we propose the Low‐Rank Isomap (LRI) algorithm by introducing a projection operator on the embedded graph from the ambient space to a low‐rank latent space to facilitate applying the partial eigenvalue decomposition. This approach leads to reducing the complexity of Isomap to a linear order while preserving the structural information during the dimensionality reduction process as long as the number of observations remains extensively larger than the dimensionality of the ambient space. The superiority of the LRI algorithm compared to some state‐of‐art algorithms is experimentally verified on facial image clustering in terms of speed and accuracy. [ABSTRACT FROM AUTHOR]

The paper studies numerical properties of LU and incomplete LU factorizations applied to the discrete linearized incompressible Navier-Stokes problem also known as the Oseen problem. A commonly used stabilized Petrov-Galerkin finite element method for the Oseen problem leads to the system of algebraic equations having a 2 × 2-block structure. While enforcing better stability of the finite element solution, the Petrov-Galerkin method perturbs the saddle-point structure of the matrix and may lead to less favorable algebraic properties of the system. The paper analyzes the stability of the LU factorization. This analysis quantifies the effect of the streamline upwind Petrov-Galerkin stabilization in terms of the perturbation made to a nonstabilized system. The further analysis shows how the perturbation depends on the particular finite element method, the choice of stabilization parameters, and flow problem parameters. The analysis of LU factorization and its stability helps to understand the properties of threshold ILU factorization preconditioners for the system. Numerical experiments for a model problem of blood flow in a coronary artery illustrate the performance of the threshold ILU factorization as a preconditioner. The dependence of the preconditioner properties on the stabilization parameters of the finite element method is also studied numerically. [ABSTRACT FROM AUTHOR]

Image segmentation has gained increasing popularity and has been widely applied in various image processing tasks recently. A simple linear iterative clustering (SLIC) superpixel generating algorithm for optical images based on k-means clustering approach works well in terms of computational simplicity and segmentation speed. However, due to the inherent speckle noise, it may generate poor segmentations for synthetic aperture radar (SAR) images. In this paper, an improved similarity measure combining pixel intensity and location similarity with edge information is utilised to replace the Euclidean distance in CIELAB colour space for performing local clustering to generate superpixels by using SLIC. Additionally, a constructed image is used to perform the superpixel cosegmentation, simultaneously segmenting the SAR image pairs. The generated superpixels can be taken as basic units for the subsequent change detection. The experimental results conducted on one simulated dataset and one real-world SAR dataset demonstrate the feasibility and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Compared to traditional transformer, power electronic transformer (PET) has a better control ability as it can manage the terminal power independently. This makes it very promising for modern power distribution systems with high penetration of renewable energy. However, the unique structure of PET increases the coupling between AC and DC network, which enhances the complexity of the traditional alternating iterative method in an AC–DC network. Since the structure of PET is based on power electronics, the power losses will influence the OPF results and have to be taken into account. This paper proposes a novel extension branch model with an accurate PET power loss model that can solve the AC–DC power flow problem in a unified way. In this method, a branch model of PET with power loss is first established. The AC and DC branches are then combined to generate an extended branch model of the whole AC–DC network. An AC–DC hybrid test system connected by two 3-port PET is used to verify the effectiveness of the proposed model via simulations. The results show that this method has a superior convergence speed than the alternating iterative model. [ABSTRACT FROM AUTHOR]

Many applications of Distribution Management Systems (DMSs) are based on power flow solutions. Fast and robust power flow methods capable of accommodating systems of general topologies and the most common models of Distributed Energy Resources (DERs) are, therefore, becoming indispensable. In this context, this paper proposes contributions for the symmetrical component‐based three‐phase power flow methods for distribution system analysis. The introduction of symmetrical components in the three‐phase power flow problem allows it to be decomposed into three single‐phase problems, which can be solved iteratively. Such decomposition significantly expedites the power flow solution problem, simplifies implementation complexity, and makes way for parallel computing techniques. The accuracy and validity of the proposed method were tested on distribution test feeders of different sizes and topologies and the results of several case studies were compared with those obtained by the Sequence Newton–Raphson method, and by the OpenDSS. Contributions of the paper include: (i) A new formulation of the Sequence‐Decoupling Compensation method in terms of real‐valued matrices; (ii) a novel modelling for PV buses; (iii) a simple procedure to tackle convergence issues related to delta and ungrounded‐wye connected transformers; and (iv) a modelling for wye, closed‐ and open‐delta connected step‐voltage regulators in the sequence frame of reference. [ABSTRACT FROM AUTHOR]

In this paper, we propose the first time fifth‐ and sixth‐order two‐step schemes. Based on the proposed two‐step methods, we develop three‐step iterative methods with the ninth‐ and tenth‐order of convergence. We also suggest two parametric families of these schemes. The obtained results are extended to i$$ i $$‐step iterations. The main advantages of the proposed methods are that they are higher order of convergence and utilize only one matrix inversion per iteration which makes these methods computationally more efficient. Numerical experiments are performed to confirm the theoretical results concerning the order of convergence and computational efficiency. [ABSTRACT FROM AUTHOR]

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughly O(N3) floating point operations (flops) for N x N pixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator to O(N2logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost of O(N2logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data. [ABSTRACT FROM AUTHOR]

Domain decomposition methods for finite element problems using a partition based on the underlying finite element mesh have been extensively studied, in this paper, we discuss algebraic extensions of the class of overlapping domain decomposition algorithms for general sparse matrices. The subproblems are created with an overlapping partition of the graph corresponding to the sparsity structure of the matrix. These algebraic domain decomposition methods are especially useful for unstructured mesh problems. We also discuss some difficulties encountered in the algebraic extension, particularly the issues related to the coarse solver. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive modification rate artificial bee colony (AMR‐ABC) algorithm is proposed by incorporating a novel adaptive modification rate to adaptively balance exploration and exploitation to determine which parameters (or the number of parameters) to be updated in a solution during each iteration. The performance of the AMR‐ABC algorithm is compared to those the standard ABC algorithm and its two variants, and the Parks–McClellan algorithm for designing Type 3 (orders: 14, 26, and 38) and Type 4 (orders: 13, 25, and 37) linear phase FIR differentiators to evaluate their design capabilities. Design results have shown that the proposed AMR‐ABC algorithm (i) outperforms four other design algorithms with the lowest p‐norm error in each of the six differentiator designs and (ii) is robust such that the same p‐norm error solution with an equiripple amplitude response in each of the six differentiator designs can be obtained by repeating a design with a different population of randomly generated initial solutions. The filter coefficients of six linear phase FIR differentiator designs are given as benchmarks to compare the p‐norm error performance of the AMR‐ABC algorithm to other algorithms. The AMR‐ABC algorithm is attractive to be used for optimisation in this and other design problems. [ABSTRACT FROM AUTHOR]

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single‐input–single‐output fractional‐order continuous‐time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional‐order continuous‐time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non‐linearity of the Wiener model part does not need to be invertible. The input and output static non‐linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional‐order continuous‐time subsystem and the input and output static non‐linear functions from the sampled input–output data by considering the system to be a multi‐input–single‐output linear fractional‐order continuous‐time model. These extra inputs represent the basis functions of the static input and output non‐linearity, where the output basis functions are simulated according to the previous estimates of the fractional‐order linear subsystem and the static input non‐linear function at every iteration. It is also possible to estimate the classical integer‐order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer‐order continuous‐time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional‐order Hammerstein–Wiener output model. [ABSTRACT FROM AUTHOR]

Summary: Iterative linear algebra methods to solve linear systems and eigenvalue problems with non‐Hermitian matrices are important for both the simulation arising from diverse scientific fields and the applications related to big data, machine learning, and artificial intelligence. The spectral property of these matrices has impacts on the convergence of these solvers. Moreover, with the increase of the size of applications, iterative methods are implemented in parallel on clusters. Analysis of their behaviors with non‐Hermitian matrices on supercomputers is so complex that we need to generate large‐scale matrices with different given spectra for benchmarking. These test matrices should be non‐Hermitian and nontrivial, with high dimension. This paper highlights a scalable matrix generator that constructs large sparse matrices using the user‐defined spectrum, and the eigenvalues of generated matrices are ensured to be the same as the predefined spectrum. This generator is implemented on CPUs and multi‐GPUs platforms, with good strong and weak scaling performance on several supercomputers. We also propose a method to verify its ability to guarantee the given spectra. Finally, we give an example to evaluate the numerical properties and parallel performance of iterative methods using this matrix generator. [ABSTRACT FROM AUTHOR]

The disparity refinement phase of existing end‐to‐end stereo matching networks refines the disparity by learning the mapping from the concatenated coarse disparity and corresponding features to fine disparity. It depends on the scenarios' characteristics, such as the distribution of disparity and semantic categories contained in the domain, which makes the network fail to work on unseen domain. In this paper, we propose a geometry and context guided refinement network (GCGR‐Net) containing a Fine Matching module and an Upsampling module. GCGR‐Net learns to utilize pixels' relationship to get high resolution dense disparity, which is independent of the data's content. The Fine Matching module performs a minimum range search based on the relationship between the possible matching pixel pairs, i.e. the called geometry information, to recover the internal structure of the object. The Upsampling module obtains context information, the relationship between central pixel and the pixels in its neighborhood, to upsample the lower resolution disparity. The final disparity map is obtained step by step through an iterative refinement model. Experiment results show that our method not only has good performance in the training scenarios, but also outperforms previous methods on the unseen domain without fine‐tuning. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of solving initial value problems and boundary value problems through the point of view of its continuous form. It is well known that in most cases these types of problems are solved numerically by performing a discretization and applying the finite difference technique to approximate the derivatives, transforming the equation into a finite‐dimensional nonlinear system of equations. However, we would like to focus on the continuous problem, and therefore, we try to set the domain of existence and uniqueness for its analytic solution. For this purpose, we study the semilocal convergence of a Newton‐type method with frozen first derivative in Banach spaces. We impose only the assumption that the Fréchet derivative satisfies the Lipschitz continuity condition and that it is bounded in the whole domain in order to obtain appropriate recurrence relations so that we may determine the domains of convergence and uniqueness for the solution. Our final aim is to apply these theoretical results to solve applied problems that come from integral equations, ordinary differential equations, and boundary value problems. [ABSTRACT FROM AUTHOR]

In most of the earlier research for multiple zeros, in order to obtain a new iteration function from the existing scheme, the usual practice is to make no change at the first substep. In this paper, we explore the idea that what are the advantages if the flexibility of choice is also given at the first substep. Therefore, we present a new two‐point sixth‐order scheme for multiple roots (m>1). The main advantages of our scheme over the existing schemes are flexibility at both substeps, simple body structure, smaller residual error, smaller error difference between two consecutive iterations, and smaller asymptotic error constant. The development of the scheme is based on midpoint formula and weight functions of two variables. We compare our methods with the existing methods of the same order with real‐life applications as well as standard test problems. From the numerical results, we find that our methods can be considered as better alternates for the existing methods of the same order. Finally, dynamical study of the proposed schemes is presented that confirms the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is intended to give an effective coordination method between high penetration of plug in electric vehicles (PEVs) and optimal operation management (OOM) of distribution network problem. An effective fuzzy logic controller (FLC) is proposed which focuses on coordinated smart charge/discharge control of high penetration of PEVs with OOM in an iterative optimization process. In each iteration, the proposed FLC receives the voltage of the connection node of the PEVs, the remaining time to the peak load and the available energy of the PEVs while appropriately specifies the amount of absorbed or injected active power of the PEVs. This coordination leads to the minimization of the electric network losses, voltage flattening and reducing the produced pollutant. A modified version of Sine‐Cosine Algorithm (MSCA) is used to minimize the objective functions while the problem constraints are satisfied. An appropriate 33‐bus distribution network with 1000 PEVs in 100 groups is considered in order to show the authenticity and efficiency of this work. The results show that the proposed FLC‐based coordination procedure could effectively adjust the exchange power of the PEVs with the OOM decision variables in an acceptable time duration. [ABSTRACT FROM AUTHOR]

Graph‐based transductive learning (GTL) is the efficient semi‐supervised learning technique which is always employed in that sufficient labeled samples can not be obtained. Conventional GTL methods generally construct a inaccurate graph in feature domain and they are not able to align feature information with label information. To address these issues, we propose an approach called Progressive Graph‐based subspace transductive learning (PGSTL) in this paper. PGSTL gradually find the intrinsic relationship between samples that more accurately aligns feature with label. Meanwhile, PGSTL develops a feature affinity matrix in the subspace of original high‐dimensional feature space, which effectively reduce the interference of noise points. And then, the representative relation matrix and the feature affinity matrix are optimized by iterative optimization strategy and finally aligned. In this way, PGSTL can not only effectively reduce the interference of noisy points, but also comprehensively consider the information in the feature and label domain of data. Extensive experimental results on various benchmark datasets demonstrate that the PGSTL achieves the best performance compared to some state‐of‐the‐art semi‐supervised learning methods. [ABSTRACT FROM AUTHOR]

In this paper, we derive two general adaptive methods with memory in the class of Newton‐type methods by modifying and introducing one and two self accelerators over a variant of Ostrowski's method. The idea of introducing adaptive self‐accelerator (via all the old information for Newton‐type methods) is new and efficient in order to obtain a higher high efficiency index. Finally, we provide convergence analysis and numerical implementations to show the feasibility and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

As the radar system tends to be complex, obtaining well-focused images with discontinued apertures becomes a challenge. Here, a new sparse aperture inverse synthetic aperture radar (SA-ISAR) imaging approach through the signal recovery method is proposed. Considering the available samples of data sets as fixed values and the missing samples as variables, the algorithm employs a gradient-based method to approach the true values of missing samples by iterations. The algorithm can recover the complete signals with a high precision. Experiments based on the measured data are carried out to validate the superiority of the novel algorithm. [ABSTRACT FROM AUTHOR]

Purpose: Recent applications of iterative image reconstruction algorithms to multislice helical CT have shown that iterative reconstruction can significantly improve image quality and reduce artifacts. In this paper, the authors introduce a combination of two different algorithms with different convergence properties: ordered subsets separable paraboloidal surrogates (OS-SPS) and iterative coordinate descent (ICD). The first one updates image voxels simultaneously, slightly changing attenuation values iteration by iteration. The second algorithm updates image voxel by voxel, each time performing full forward and backward projections of the voxel. It has been shown that ICD converges better at high-frequency areas and requires more iterations to reconstruct low-frequency components of the image. In contrast to ICD, SPS requires multiple iterations to reconstruct high-frequency areas. In this paper, the authors introduce an algorithm which leverages the benefits of both ICD and SPS. Methods: The idea is to update the entire image with SPS, determine high-frequency components, and focus ICD computations on it using nonhomogeneous ICD update. Results: The authors have successfully implemented OS-SPS, ICD, their hybrid approach, and few variations of ICD based on spatially nonuniform updates. Conclusions: The authors have examined the convergence of different algorithms and found that proposed algorithm converges better than OS-SPS, ICD, as well as various improved variants of ICD. [ABSTRACT FROM AUTHOR]

Purpose: Phantom-based objective image quality assessment methods are widely used in the medical physics community. For a filtered backprojection (FBP) reconstruction-based linear or quasilinear imaging system, the use of this methodology is well justified. Many key image quality metrics acquired with phantom studies can be directly applied to in vivo human subject studies. Recently, a variety of image quality metrics have been investigated for model-based iterative image reconstruction (MBIR) methods and several novel characteristics have been discovered in phantom studies. However, the following question remains unanswered: can certain results obtained from phantom studies be generalized to in vivo animal studies and human subject studies? The purpose of this paper is to address this question. Methods: One of the most striking results obtained from phantom studies is a novel power-law relationship between noise variance of MBIR (σ²) and tube current-rotation time product (mAs): σ² ∝ (mAs)-0.4 [K. Li et al., "Statistical model based iterative reconstruction (MBIR) in clinical CT systems: Experimental assessment of noise performance," Med. Phys. 41, 041906 (15pp.) (2014)]. To examine whether the same power-law works for in vivo cases, experimental data from two types of in vivo studies were analyzed in this paper. All scans were performed with a 64-slice diagnostic CT scanner (Discovery CT750 HD, GE Healthcare) and reconstructed with both FBP and a MBIR method (Veo, GE Healthcare). An Institutional Animal Care and Use Committee-approved in vivo animal study was performed with an adult swine at six mAs levels (10-290). Additionally, human subject data (a total of 110 subjects) acquired from an IRB-approved clinical trial were analyzed. In this clinical trial, a reduced-mAs scan was performed immediately following the standard mAs scan; the specific mAs used for the two scans varied across human subjects and were determined based on patient size and clinical indications. The measurements of σ² were performed at different mAs by drawing regions-of-interest (ROIs) in the liver and the subcutaneous fat. By applying a linear least-squares regression, the β values in the power-law relationship σ² ∝ (mAs)-β were measured for the in vivo data and compared with the value found in phantom experiments. Results: For the in vivo swine study, an exponent of &#946 = 0.43 was found for MBIR, and the coefficient of determination (R²) for the corresponding least-squares power-law regression was 0.971. As a reference, the β and R² values for FBP were found to be 0.98 and 0.997, respectively, from the same study, which are consistent with the well-known σ² ?∝ (mAs)-1.0 relationship for linear CT systems. For the human subject study, the measured β values for the MBIR images were 0.41?±0.12 in the liver and 0.37?±0.12 in subcutaneous fat. In comparison, the β values for the FBP images were 1.04±0.10 in the liver and 0.97±0.12 in subcutaneous fat. The β values of MBIR and FBP obtained from the in vivo studies were found to be statistically equivalent to the corresponding β values from the phantom study within an equivalency interval of [-0.1, 0.1] (p < 0.05); across MBIR and FBP, the difference in β was statistically significant (p < 0.05). Conclusions: Despite the nonlinear nature of the MBIR method, the power-law relationship, σ² ẙ (mAs)-0.4, found from phantom studies can be applied to in vivo animal and human subject studies. [ABSTRACT FROM AUTHOR]

In a very interesting recent paper, the authors illustrated an improved analysis of orthogonal matching pursuit in the general perturbation model y=Φ+Ex+n, where E is the measurement perturbation. This comment will point out that there are some errors in that paper. [ABSTRACT FROM AUTHOR]

Asynchronous iterations often converge under different conditions than their synchronous counterparts. In this paper we will study the global convergence of Jacobi-Newton-like methods for nonlinear equations Fx = 0. It is a known fact, that the synchronous algorithm converges monotonically, if F is a convex M-function and the starting values x0 and y0 meet the condition Fx0 ≤ 0 ≤ Fy0. In the paper it will be shown, which modifications are necessary to guarantee a similar convergence behavior for an asynchronous computation. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The compressed sensing (CS) radar receiver based on the theory of CS has a great advantage in receiving wide-band signal and can receive high-frequency radar signal at a sampling rate far lower than the traditional receiver. However, in order to obtain the information of the target signal, the parameters of the reconstructed signal still need to be measured by conventional methods. In order to make full use of the compressed sampling and the characteristics of radar signals, this study proposed a cascading dictionary matching pursuit algorithm based on block-sparsity (BS-CDMP) to achieve fast identification and reconstruction of received signals. First, a signal-level redundant dictionary is constructed for quickly identifying the signal in which the authors are interested in. Then, they study the feasibility of cascading the signal-level redundant dictionary and the DFT basis as a whole sparsity dictionary. Finally, the block sparsity is introduced for the selection of different parts of the dictionary during greedy iteration. Experimental results show that their proposed algorithm has considerable and universal reconfiguration performance and can directly perform fast reconstruction and recognition of the target signal. [ABSTRACT FROM AUTHOR]

Ladder network parameters identification of transformer winding based on frequency response analysis data is crucial to winding fault diagnosis. In the authors' previous study, the Gauss–Newton iteration algorithm (GNIA) had been proposed to efficiently identify the network parameters. The core in GNIA is the Jacobian matrix, composed of derivative of frequency response function (FRF) to network components. This study proposes a generic algorithm to calculate this Jacobian matrix. Two key problems concerning the algorithm are solved elaborately. The first problem is the method for derivative calculation toward an arbitrary FRF based on adjoint network method (ANM). The other issue is the mathematical model construction of double ladder network and its adjoint network toward different FRFs to obtain all network branch voltages and currents, which are required in the derivative calculation by ANM. This generic algorithm can efficiently and effectively calculate the Jacobian matrix, which can be applied on ladder network parameters identification and winding fault diagnosis. [ABSTRACT FROM AUTHOR]

Many practical problems in the real world can be formulated as the non‐negative ℓ0 ‐minimisation problems, which seek the sparsest non‐negative signals to underdetermined linear equations. They have been widely applied in signal and image processing, machine learning, pattern recognition and computer vision. Unfortunately, this non‐negative ℓ0 ‐minimisation problem is non‐deterministic polynomial hard (NP‐hard) because of the discrete and discontinuous nature of the ℓ0 ‐norm. Inspired by the good performances of the fraction function in the authors' former work, in this paper, the authors replace the ℓ0 ‐norm with the non‐convex fraction function and study the minimisation problem of the fraction function in recovering the sparse non‐negative signal from an underdetermined linear equation. They discuss the equivalence between non‐negative ℓ0 ‐minimisation problem and non‐negative fraction function minimisation problem, and the equivalence between non‐negative fraction function minimisation problem and regularised non‐negative fraction function minimisation problem. It is proved that the optimal solution to the non‐negative ℓ0 ‐minimisation problem could be approximately obtained by solving their regularised non‐negative fraction function minimisation problem if some specific conditions are satisfied. Then, they propose a non‐negative iterative thresholding algorithm to solve their regularised non‐negative fraction function minimisation problem. At last, numerical experiments on some sparse non‐negative signal recovery problems are reported. [ABSTRACT FROM AUTHOR]

Purpose: Signal detection on 3D medical images depends on many factors, such as foveal and peripheral vision, the type of signal, and background complexity, and the speed at which the frames are displayed. In this paper, the authors focus on the speed with which radiologists and naïve observers search through medical images. Prior to the study, the authors asked the radiologists to estimate the speed at which they scrolled through CT sets. They gave a subjective estimate of 5 frames per second (fps). The aim of this paper is to measure and analyze the speed with which humans scroll through image stacks, showing a method to visually display the behavior of observers as the search is made as well as measuring the accuracy of the decisions. This information will be useful in the development of model observers, mathematical algorithms that can be used to evaluate diagnostic imaging systems. Methods: The authors performed a series of 3D 4-alternative forced-choice lung nodule detection tasks on volumetric stacks of chest CT images iteratively reconstructed in lung algorithm. The strategy used by three radiologists and three naïve observers was assessed using an eye-tracker in order to establish where their gaze was fixed during the experiment and to verify that when a decision was made, a correct answer was not due only to chance. In a first set of experiments, the observers were restricted to read the images at three fixed speeds of image scrolling and were allowed to see each alternative once. In the second set of experiments, the subjects were allowed to scroll through the image stacks at will with no time or gaze limits. In both static-speed and free-scrolling conditions, the four image stacks were displayed simultaneously. All trials were shown at two different image contrasts. Results: The authors were able to determine a histogram of scrolling speeds in frames per second. The scrolling speed of the naïve observers and the radiologists at the moment the signal was detected was measured at 25-30 fps. For the task chosen, the performance of the observers was not affected by the contrast or experience of the observer. However, the naïve observers exhibited a different pattern of scrolling than the radiologists, which included a tendency toward higher number of direction changes and number of slices viewed. Conclusions: The authors have determined a distribution of speeds for volumetric detection tasks. The speed at detection was higher than that subjectively estimated by the radiologists before the experiment. The speed information that was measured will be useful in the development of 3D model observers, especially anthropomorphic model observers which try to mimic human behavior. [ABSTRACT FROM AUTHOR]

Purpose: An iterative reconstruction method has been previously reported by the authors of this paper. However, the iterative reconstruction method was demonstrated by solely using the numerical simulations. It is essential to apply the iterative reconstruction method to practice conditions. The objective of this work is to validate the capability of the iterative reconstruction method for reducing the effects of acoustic heterogeneity with the experimental data in microwave induced thermoacoustic tomography. Methods: Most existing reconstruction methods need to combine the ultrasonic measurement technology to quantitatively measure the velocity distribution of heterogeneity, which increases the system complexity. Different to existing reconstruction methods, the iterative reconstruction method combines time reversal mirror technique, fast marching method, and simultaneous algebraic reconstruction technique to iteratively estimate the velocity distribution of heterogeneous tissue by solely using the measured data. Then, the estimated velocity distribution is used subsequently to reconstruct the highly accurate image of microwave absorption distribution. Experiments that a target placed in an acoustic heterogeneous environment are performed to validate the iterative reconstruction method. Results: By using the estimated velocity distribution, the target in an acoustic heterogeneous environment can be reconstructed with better shape and higher image contrast than targets that are reconstructed with a homogeneous velocity distribution. Conclusions: The distortions caused by the acoustic heterogeneity can be efficiently corrected by utilizing the velocity distribution estimated by the iterative reconstruction method. The advantage of the iterative reconstruction method over the existing correction methods is that it is successful in improving the quality of the image of microwave absorption distribution without increasing the system complexity. [ABSTRACT FROM AUTHOR]

Purpose: Validating the usage of deformable image registration (DIR) for daily patient positioning is critical for adaptive radiotherapy (RT) applications pertaining to head and neck (HN) radiotherapy. The authors present a methodology for generating biomechanically realistic ground-truth data for validating DIR algorithms for HN anatomy by (a) developing a high-resolution deformable biomechanical HN model from a planning CT, (b) simulating deformations for a range of interfraction posture changes and physiological regression, and (c) generating subsequent CT images representing the deformed anatomy. Methods: The biomechanical model was developed using HN kVCT datasets and the corresponding structure contours. The voxels inside a given 3D contour boundary were clustered using a graphics processing unit (GPU) based algorithm that accounted for inconsistencies and gaps in the boundary to form a volumetric structure. While the bony anatomy was modeled as rigid body, the muscle and soft tissue structures were modeled as mass-spring-damper models with elastic material properties that corresponded to the underlying contoured anatomies. Within a given muscle structure, the voxels were classified using a uniform grid and a normalized mass was assigned to each voxel based on its Hounsfield number. The soft tissue deformation for a given skeletal actuation was performed using an implicit Euler integration with each iteration split into two substeps: one for the muscle structures and the other for the remaining soft tissues. Posture changes were simulated by articulating the skeletal structure and enabling the soft structures to deform accordingly. Physiological changes representing tumor regression were simulated by reducing the target volume and enabling the surrounding soft structures to deform accordingly. Finally, the authors also discuss a new approach to generate kVCT images representing the deformed anatomy that accounts for gaps and antialiasing artifacts that may be caused by the biomechanical deformation process. Accuracy and stability of the model response were validated using ground-truth simulations representing soft tissue behavior under local and global deformations. Numerical accuracy of the HN deformations was analyzed by applying nonrigid skeletal transformations acquired from interfraction kVCT images to the model's skeletal structures and comparing the subsequent soft tissue deformations of the model with the clinical anatomy. Results: The GPU based framework enabled the model deformation to be performed at 60 frames/s, facilitating simulations of posture changes and physiological regressions at interactive speeds. The soft tissue response was accurate with a R² value of >0.98 when compared to ground-truth global and local force deformation analysis. The deformation of the HN anatomy by the model agreed with the clinically observed deformations with an average correlation coefficient of 0.956. For a clinically relevant range of posture and physiological changes, the model deformations stabilized with an uncertainty of less than 0.01 mm. Conclusions: Documenting dose delivery for HN radiotherapy is essential accounting for posture and physiological changes. The biomechanical model discussed in this paper was able to deform in real-time, allowing interactive simulations and visualization of such changes. The model would allow patient specific validations of the DIR method and has the potential to be a significant aid in adaptive radiotherapy techniques. [ABSTRACT FROM AUTHOR]

SUMMARY This paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil-structure interaction problems in the frequency domain. The application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods. Three coupling methodologies are presented and their computational performance is assessed through numerical examples. It is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient, as it requires the assembly of a dynamic soil stiffness matrix. Iterative solution procedures are presented as well, and it is shown that the application of such schemes to dynamic soil-structure interaction problems in the frequency domain is not trivial, as convergence can hardly be achieved if no relaxation procedure is incorporated. Aitken's Δ2-method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter, while a novel relaxation technique is proposed for parallel iterative algorithms. It is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain; the fastest convergence is observed if Neumann boundary conditions are imposed on the stiffest subdomain. The use of a dedicated solver for each subdomain hence results in a reduced computational effort. A monolithic coupling strategy, often used for the solution of fluid-structure interaction problems, is also introduced. The governing equations are simultaneously solved in this approach, while the assembly of a dynamic soil stiffness matrix is avoided. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Interactive rigid body simulation is an important part of many modern computer tools, which no authoring tool nor game engine can do without. Such high-performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems. This paper is a self contained state-of-the-art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which have evolved and matured over the past 20 years. Furthermore, the paper communicates the mathematical and theoretical details in a pedagogical manner. This paper is not only a stake in the sand on what has been done, it also seeks to give the reader deeper insights to help guide their future research. [ABSTRACT FROM AUTHOR]

Systematic Reviews (SRs) have recently intensified in Software Engineering. However, there is a lack of work that makes explicit how the process to perform SR is in practice. The goal of this paper is externalising the process that reflects how SRs are currently performed, transforming tacit knowledge into explicit knowledge. We describe the phases and activities that compose the process and the relationship among them, and explore the iterative characteristic of this process, focusing on intra‐ and inter‐phase iterations that are necessary to conduct the process appropriately. To achieve the proposed goal, we devised the process based on practical experience acquired for several years by research groups in Software Engineering, which include graduate students and researchers who have applied SR. The process has been applied in several SRs and seems to be effective in keeping the focus of the review at all phases. Moreover, the externalisation of the process has been useful to help researchers improving the process execution quality. As the process reflects the practice and is explained in details, it can be used as a guide to better understand the SR process and its details. This shall contribute to improve all SR process phases, and hence the quality of SR results. [ABSTRACT FROM AUTHOR]

Incentive regulations of reliability have made a link between distribution companies' revenue and their service reliability. The companies have to decide how much to spend on various projects to provide an acceptable level of reliability while anticipation of load growth. Planners and decision makers require a comprehensive framework to optimally allocate available budgets to different plans with the highest benefits considering implementation of incentive regulation. This paper proposes a decision framework for the optimum share of expansion and reliability oriented plans in presence of reward–penalty mechanisms. A two‐layer optimization model is introduced, where in the outer layer, an iterative algorithm is applied to determine the optimal set of long‐term projects including Distributed Generations (DGs) installation. A heuristic optimization algorithm is employed in this layer. Considering long‐term plans, in inner optimization layer, the optimal set of mid‐term plans including feeder reinforcement, and preventive maintenance actions are determined using algorithms such as Branch‐and‐Cut and dynamic programming techniques. The model is further implemented on a test distribution network and the results are investigated through various case studies. Obtained results show the strong influence of incentive regulation on reliability indices. [ABSTRACT FROM AUTHOR]

Denoising is one of the core steps in seismic data processing flow. The seismic gather consists of multiple traces captured at different receivers. A set of receivers observe waves which are reflected from the same reflection point. Those traces need to be grouped together as they contain the same information about the earth subsurface layers. This is done by finding a common mid‐point (CMP) between the source and geophones. The time delay between CMP gathered traces are corrected by the normal move out correction method but the individual traces are corrupted by noise. In this paper we, propose a method for denoising individual traces. The set of traces can be modelled as belonging to a low‐dimensional subspace of an ambient signal space. This allows for construction of sparse representations of each trace in terms of other traces in the CMP gather. The resulting sparse representations are subsequently utilised to construct approximations of individual traces and thus, noise is suppressed. We constructed, the approximations using orthogonal matching pursuit. We applied proposed method to synthetic and field seismic data, the proposed technique performs better on established benchmarks while capturing the true locations of weak reflections and effectively attenuating the random noise. [ABSTRACT FROM AUTHOR]

In this paper, a new technique for plane detection from 3D point clouds is proposed. The algorithm depends on two concepts to balance between high‐accuracy and fast performance. The first is the use of a new fast octree‐based balanced density down‐sampling technique to reduce the number of points. The second is the fact that the number of planes in any dataset is much less than the number of the points. Random points are examined to find the 3D planes. To increase the accuracy, the system utilizes an adaptive plane extraction technique to overcome data noise. Initially, the point cloud is subdivided using octree into small cubes with a limited number of points. Then the cubes are down‐sampled based on the local density of each cube. The points are explored randomly for finding a planar surface by applying principal component analysis (PCA) on the points' spherical neighborhood obtained by the down‐sampled octree structure. The adaptive plane extraction is used to adjust the plane orientation to find the best position that includes the maximum number of points. Experimental results demonstrate that the proposed algorithm is capable of processing large amounts of data efficiently to produce accurate results that are robust to noise. [ABSTRACT FROM AUTHOR]

Over a transformer's operational lifetime, the moisture content of its insulation pressboard increases because of the ageing of its internal insulation. Thus, this moisture content becomes an important index for judging the ageing of this insulation. In this study, to analyse the moisture content of a transformer's insulation pressboard using the dielectric response insulation technique, the XY‐equivalent model analysis method for classical transformers is combined with a dielectric‐constant algorithm for mixed media. In addition, a new method for calculating the moisture content of a pressboard is obtained via cyclic iterative comparison calculations based on the dielectric response translation formula, the temperature, and the material activation energy. The XY‐equivalent models of transformers with various proportions are derived under laboratory conditions. The moisture contents of the transformers' insulating pressboards are obtained under the corresponding dielectric loss factor curves by using the proposed moisture content calculation method, which provides a result that is within 4.83% of that provided by the IDAX‐300 moisture content analysis algorithm, thus demonstrating its validity. [ABSTRACT FROM AUTHOR]

This paper automatizes the process of bone age maturity assessment by applying three versions of particle swarm optimization (PSO) along with image processing methods to the left hand X‐ray images. PSO versions were adopted to enhance the segmentation accuracy. The proposed method was compared to the conventional visual inspection method in terms of three segmentation criteria, classification accuracy, robustness against noise and computational complexity. Herein, PSO, worst behavior‐based PSO (WB‐PSO) and adaptive inertia weight (AIW‐PSO) along with Otsu and an iteratively statistical method were implemented to segment the hand radiographs. A dataset containing left hand‐wrist radiographs from 65 referred children was collected. Their results provided 82.49, 83.08, 84.27, 81.76 and 69.04% classification accuracy using the PSO, WB‐PSO, AIW‐PSO, Otsu and the iteratively statistical methods, respectively. To assess the robustness of the implemented methods, white Gaussian noise with different intensities was added to the images and the results indicated that as the noise level increased the robustness against noise for the PSO variants became more highlighted compared to the Otsu and statistical methods. Due to the convincing results, the AIW‐PSO image segmentation system is suggested as an auxiliary diagnostic tool to help specialists for more accurate age bone estimation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a new singular value decomposition (SVD) called weighted SVD (WSVD) using a new inner product instead of the Euclidean one. We use the WSVD to approximate the singular values and the singular functions of the Fredholm integral operators. In this case, the new inner product arises from the numerical integration used to discretize the operator. Then, the truncated WSVD (TWSVD) is used to regularize the Nyström discretization of the first-kind Fredholm integral equations. Also, we consider the weighted LSQR (WLSQR) to approximate the solution obtained by the TWSVD method for large problems. Numerical experiments on a few problems are used to illustrate that the TWSVD can perform better than the TSVD. [ABSTRACT FROM AUTHOR]

The optimal power flow (OPF) problem for active distribution networks with distributed generation (DG) and a variety of discretely adjustable devices (e.g. on‐load tap‐changers, OLTCs) is essentially a non‐convex, non‐linear, mixed‐integer optimisation problem. In this study, the quadratic model of three‐phase OLTCs is proposed by adding branch currents as unknown variables, which guarantee a constant Hessian matrix throughout iterations. This study proposes a three‐phase OPF model for active distribution networks, considering a three‐phase DG model. The OPF model is solved by an interior point method incorporating a quadratic penalty function as opposed to a Gaussian penalty function. Furthermore, a voltage regulator is also incorporated into the OPF model to form an integrated regulation strategy. The methodology is tested and validated on the IEEE 13‐bus three‐phase unbalanced test system. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is on the convergence analysis for two-grid and multigrid methods for linear systems arising from conforming linear finite element discretization of the second-order elliptic equations with anisotropic diffusion. The multigrid algorithm with a line smoother is known to behave well when the discretization grid is aligned with the anisotropic direction; however, this is not the case with a nonaligned grid. The analysis in this paper is mainly focused on two-level algorithms. For aligned grids, a lower bound is given for a pointwise smoother, and this bound shows a deterioration in the convergence rate, whereas for 'maximally' nonaligned grids (with no edges in the triangulation parallel to the direction of the anisotropy), the pointwise smoother results in a robust convergence. With a specially designed block smoother, we show that, for both aligned and nonaligned grids, the convergence is uniform with respect to the anisotropy ratio and the mesh size in the energy norm. The analysis is complemented by numerical experiments that confirm the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Bootstrap algebraic multigrid (BAMG) is a multigrid-based solver for matrix equations of the form Ax=b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax=0, and are then possibly improved later using a multilevel eigensolver. This paper introduces a flexible variant of BAMG that determines the interpolation weights indirectly by ‘collapsing’ the unwanted connections in ‘operator interpolation’. Compared to BAMG, this indirect BAMG approach (iBAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant. This paper studies the numerical performance of iBAMG and establishes an equivalence, under certain assumptions, between it and a slightly modified (standard) BAMG scheme. To focus on camparing BAMG and iBAMG and exposing their behavior as the problem size grows, the numerical experiments concentrate on Poisson-like scalar problems. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a novel class of preconditioners for the iterative solution of the sequence of symmetric positive-definite linear systems arising from the numerical discretization of transient parabolic and self-adjoint partial differential equations. The preconditioners are obtained by nesting appropriate projections of reduced-order models into the classical iteration of the preconditioned conjugate gradient (PCG). The main idea is to employ the reduced-order solver to project the residual associated with the conjugate gradient iterations onto the space spanned by the reduced bases. This approach is particularly appealing for transient systems where the full-model solution has to be computed at each time step. In these cases, the natural reduced space is the one generated by full-model solutions at previous time steps. When increasing the size of the projection space, the proposed methodology highly reduces the system conditioning number and the number of PCG iterations at every time step. The cost of the application of the preconditioner linearly increases with the size of the projection basis, and a trade-off must be found to effectively reduce the PCG computational cost. The quality and efficiency of the proposed approach is finally tested in the solution of groundwater flow models. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]