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Summary: This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a structure‐preserving model reduction method for second‐order systems based on H2 optimal interpolation. In the iterative process of the proposed method, an algorithm is presented for selecting interpolation points in order to control the dimension of the reduced system. Result about error analysis of the interpolation points selection algorithm is obtained and the property of the new model reduction method is also given. Finally, three numerical examples are performed to illustrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

This paper considers the iterative parameter estimation for a dual‐rate sampled‐data bilinear system with autoregressive moving average noise. Through combining the auxiliary model identification idea with the data filtering technique, this paper derives two filtering auxiliary model gradient‐based iterative algorithms by using two different filters. The key is to construct an auxiliary model for predicting the unavailable outputs, and to transform the dual‐rate bilinear system identification model into two sub‐identification models. Finally, an auxiliary model gradient‐based iterative (AM‐GI) algorithm is presented for comparison. The simulation results indicate that the proposed algorithms are effective for identifying the dual‐rate sampled‐data bilinear systems, and can generate more accurate parameter estimates and have a higher computational efficiency than the AM‐GI algorithm. [ABSTRACT FROM AUTHOR]

SUMMARY The paper proposes a cooperative group location (CGL) scheme to solve the ill-conditioned location problem in mobile communication networks, which means that the mobile terminal (MT) has no sufficient signal resources from the networks to uniquely localize itself. On the basis of rigid graph theory, the unique solvability of the CGL scheme is completely proved in the theory in this paper. In CGL, it is assumed that the different MTs can directly communicate with each other in a peer-to-peer manner and form a terminal group (TG), which is propelled by some distinct characteristics of next-generation wireless networks such as ubiquitous inter-net and inter-communicating, device-to-device connectivity, and so on. When each MT in a TG has no sufficient signal resources, the CGL scheme makes it possible to accurately locate all the MTs in the TG. Two CGL-based location algorithms-improved Taylor-series iteration location algorithm and search and positioning algorithm, are presented in this paper. The numerical simulation results indicate that the proposed algorithms have higher positioning accuracy over traditional geometric location methods in ill conditions. The CGL scheme can effectively enhance the robustness and precision of localization and provide a novel idea to the positioning of MTs in next-generation mobile communication networks. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The block Wiedemann (BW) algorithm is frequently used to solve sparse linear systems over GF(2). Iterative sparse matrix-vector multiplication is the most time-consuming operation. The necessity to accelerate this step is motivated by the application of BW to very large matrices used in the linear algebra step of the number field sieve (NFS) for integer factorization. In this paper, we derive an efficient CUDA implementation of this operation by using a newly designed hybrid sparse matrix format. This leads to speedups between 4 and 8 on a single graphics processing unit (GPU) for a number of tested NFS matrices compared with an optimized multicore implementation. We further present a GPU cluster implementation of the full BW for NFS matrices. A small-sized GPU cluster is able to outperform CPU clusters of larger size for large matrices such as the one obtained from the Kilobit special NFS factorization. [ABSTRACT FROM AUTHOR]

We envision a large-scale multiclass optical network in which lightpaths are dynamically set up and terminated between source and destination nodes and these lightpaths traverse through a number of interconnected WDM networks in different administrative domains. In this envisioned multiclass network, calls are classified by the number of wavelengths demanded per call and the statistics of call holding times (or service subscription periods). We present an approximation method for the performance analysis of such a large-scale multiclass optical WDM network. We model the large-scale optical network as a two-level hierarchical multiclass loss network; the lower level of hierarchy consists of individual optical WDM networks (network segments). Each of these network segments is abstracted to a logical node at the higher level of hierarchy, and these logical nodes are connected to each other through logical links. We also assume that the call processing mechanism in this large-scale optical network resorts to hierarchical routing. The algorithms presented in this paper compute per-class end-to-end approximate blocking probabilities. Our experiments show that the simulation results match closely with the results of the proposed analytical approximation methods, thus validating the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd. For multiclass optical WDM networks, we developed and tested novel algorithms that efficiently compute approximate perclass blocking probabilities by employing reduced-load approximation and fixedpoint iterations, and our earlier results showed good performance of this methodology. In the present paper, we tailor this methodology for large-scale multiclass optical WDM networks that use hierarchical routing. Then, through our extensive simulation results we show that the proposed methodology of approximation is useful even for large-scale hierarchical WDM networks. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Prony's method is an approximation approach to decomposing a function into sum of exponents and thus is applicable to unknown frequencies estimation of signals. The concrete algorithms for estimating pure sine wave, triple tone, and quadruple tone have already been derived and presented. This paper aims at deriving the estimating algorithm for multi-sine signals which consist of unknown sine waves. The new method of generating an algebraic algorithm for detecting unknown frequencies in the signals is derived by mathematical induction. The crux of the generation is dependent on the integer matrices induction. A handy method for generating the matrices is shown as well. Algorithms for the triple tone, quadruple tone, and the higher-order tone are generated and verified. As a result, they are shown to be identical to the ordinary algorithms. Subjects on the application of the induced algorithm to practical frequency detection are discussed. The algorithm has both instantaneity in the time domain and higher resolution in the frequency domain, that is, the signal analysis by the algorithm can be performed without constraint of the uncertainty principle. An iterative solution for algebraic equation is dominant for calculation in the algorithm. Techniques for detecting frequencies in a multi-sine of unknown order are also discussed. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(3): 27– 38, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20404 [ABSTRACT FROM AUTHOR]

Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which have an optimal order computational complexity with respect to the size of the system. Such methods were first presented in Axelsson and Padiy (SIAM. J. Sci. Stat. Comp. 1990; 20:1807) and Axelsson and Vassilevski (Numer. Math. 1989; 56:157), and are based on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant γ in the so-called Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. It turns out that only existence of uniform estimates for this constant is not enough but accurate quantitative bounds for γ have to be found as well. More precisely, the value of the upper bound for γ∈(0,1) is part of the construction of various multilevel extensions of the related two-level methods. In this paper, an algebraic two-level preconditioning algorithm for second-order elliptic boundary value problems is constructed, where the discretization is done using Crouzeix–Raviart non-conforming linear finite elements on triangles. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinements are not nested. To handle this, a proper two-level basis is considered, which enables us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The major contribution of this paper is the derived estimates of the related constant γ in the strengthened CBS inequality. These estimates are uniform with respect to both coefficient and mesh anisotropy. To our knowledge, the results presented in the paper are the first such estimates for non-conforming FEM systems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Bramble et al. (Math. Comput. (2000); 69 (230) : 667–689) discussed the Uzawa type algorithms for iteratively solving nonsymmetric stable saddle point problems. In this paper, we consider the Uzawa type algorithms for iteratively solving generalized saddle point problems. Our main concern is how to accelerate the convergence of the inexact Uzawa type algorithms. The contributions of the paper are that a new non-linear Uzawa type algorithm is presented and its convergence is analysed. Applications to Navier–Stokes equations by mixed finite element discretization with an unstable pair of approximation spaces, i.e. Q1-P0 pair of approximation spaces, are discussed and the results of the numerical experiments of applying our new algorithm are presented. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, power allocation over time-varying multiple-access interference channels is studied. Particularly, stochastic network sum-rate maximizing and max-min rate power allocation, and total power minimization problems are formulated, capturing the random nature of communication channels. Typically, a centralized controller must have perfect knowledge of global instantaneous channel state information for dynamic optimal power allocation; however, this may not be possible, because of the computational complexity and communication overheads/delays involved. Based on the second-order statistics of the channel state information, the stochastic problem formulations are transformed into their optimal deterministic representations in terms of ergodic capacity, while ensuring satisfactory quality of service via target outage probability. However, such deterministic reformulations happen to be non-convex and thus are computationally expensive. In turn, sub-optimal reformulations are derived and solved via iterative low-complexity algorithms. Simulation results demonstrate that the proposed deterministic sub-optimal power allocation reformulations closely coincide with their optimal deterministic and dynamic counterparts, with the proposed algorithms converging in a finite number of iterations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the field of system modeling, circuit synthesis and filter design, it is very important to approximate a given characteristic function by a rational function of an appropriate order. Padé approximation has been known for a long time and is one of the rational function approximation methods used extensively because of its simplicity. This paper proposes to investigate N-point Padé approximation, from the system-theoretic viewpoint. The N-point Padé approximation is a rational function interpolation including the derivative of arbitrary order and, compared to regular Padé approximation and rational Hermite interpolation. In this paper we discuss the following subjects on rational function approximation of given characteristic function: its explicit form, minimal order realization problem, Nuttall's compact form, its relation to continued fractions, and the numerical efficient iterative algorithm. These are more general discussions, even including regular Padé approximation. Also, we give numerical results of the approximation of a transfer function for continuous and discrete systems as an example of application of N-point Padé approximation. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example. [ABSTRACT FROM AUTHOR]

This paper introduces the iterative feedback tuning (IFT) into a Youla parameterization scheme for fault-tolerant control. By off-line IFT-experiments of tuning Youla parameters, the proposed algorithm deals with a number of conditional failures that are described by the dual Youla parameter. The main contribution of this paper is to show how Youla scheme-based IFT can be constructed for multivariable linear time-invariant systems. Particular attention is given to the issue of the structure of the Youla parameter (filter), in which both finite impulse response and infinite impulse response filters are presented and compared. As an illustration, the method is applied to a simulation model of a continuous stirred tank heater system. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF. [ABSTRACT FROM AUTHOR]

The main objective in distributed sensor networks is to reach agreement or consensus on values acquired by the sensors. A common methodology to approach this problem is using the iterative and weighted linear combination of those values to which each sensor has access. Different methods to compute appropriate weights have been extensively studied, but the resulting iterative algorithm still requires many iterations to provide a fairly good estimate of the consensus value. In this paper, different accelerating consensus approaches based on adaptive and non-adaptive filtering techniques are studied and applied on the problem of acoustic source localization using the adaptive projected subgradient method. A comparative simulation study shows that the non-adaptive polynomial filters based on Newton's interpolating polynomials and semidefinite programming can provide more accelerated consensus and better estimation accuracy than adaptive filters evaluated using constrained affine projection algorithm or stochastic gradient algorithm provided that the network topology is known beforehand. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a rapid iterative algorithm is proposed to find robust approximations for the inverse of nonsingular matrices. The analysis of convergence reveals that this high-order method possesses eighth-order convergence. The interesting point is that, this rate is attained using less number of matrix-by-matrix multiplications in contrast to the existing methods of the same type in the literature. The extension of the method for finding Moore-Penrose inverse of singular or rectangular matrices is also presented. Numerical comparisons will be given to show the applicability, stability and consistency of the new scheme by paying special attention on the computational time. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a modified gradient‐based algorithm for solving extended Sylvester‐conjugate matrix equations. The idea is from the gradient‐based method introduced in [14] and the relaxed gradient‐based algorithm proposed in [16]. The convergence analysis of the algorithm is investigated. We show that the iterative solution converges to the exact solution for any initial value based on some appropriate assumptions. A numerical example is given to illustrate the effectiveness of the proposed method and to test its efficiency and accuracy compared with those presented in [14] and [16]. [ABSTRACT FROM AUTHOR]

This paper addresses the control problem of a three-phase voltage source pulse width modulation rectifier in the presence of parametric uncertainties and external time-varying disturbances. An adaptive controller is designed by combining a modified dynamic surface control method and a predictor-based iterative neural network control algorithm. Especially, neural networks with iterative update laws based on prediction errors are employed to identify the lumped uncertainties. Besides, a finite-time-convergent differentiator, instead of a first-order filter, is used to obtain the time derivative of the virtual control law. Using a Lyapunov-Krasovskii functional, it is proved that all signals in the closed-loop system are ultimately uniformly bounded. Both simulation and experimental studies are provided to show the effectiveness of the proposed approach. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

In this paper, we present a parameter estimation procedure for a condition-based maintenance model under partial observations. Systems can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is driven by a continuous time homogeneous Markov chain and the system state is unobservable, except the failure state. Vector information that is stochastically related to the system state is obtained through condition monitoring at equidistant sampling times. Two types of data histories are available - data histories that end with observable failure, and censored data histories that end when the system has been suspended from operation but has not failed. The state and observation processes are modeled in the hidden Markov framework and the model parameters are estimated using the expectation-maximization algorithm. We show that both the pseudolikelihood function and the parameter updates in each iteration of the expectation-maximization algorithm have explicit formulas. A numerical example is developed using real multivariate spectrometric oil data coming from the failing transmission units of 240-ton heavy hauler trucks used in the Athabasca oil sands of Alberta, Canada. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper describes the development of explicit time stepping methods for linear PDEs that are specifically designed to cope with the stiffness of the system of ODEs that results from spatial discretization. As stiffness is caused by the contrasting behavior of coupled components of the solution, it is proposed to adopt a componentwise approach in which each coefficient of the solution in an appropriate basis is computed using an individualized approximation of the solution operator. This has been accomplished by Krylov subspace spectral (KSS) methods, which use techniques from 'matrices, moments and quadrature' to approximate bilinear forms involving functions of matrices via block Gaussian quadrature rules. These forms correspond to coefficients with respect to the chosen basis of the application of the solution operator of the PDE to the solution at an earlier time. In this paper, it is proposed to substantially enhance the efficiency of KSS methods through the prescription of quadrature nodes on the basis of asymptotic analysis of the recursion coefficients produced by block Lanczos iteration for each Fourier coefficient as a function of frequency. The potential of this idea is illustrated through numerical results obtained from the application of the modified KSS methods to diffusion equations and wave equations. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The aim of the nuclear norm minimization problem is to find a matrix that minimizes the sum of its singular values and satisfies some constraints simultaneously. Such a problem has received more attention largely because it is closely related to the affine rank minimization problem, which appears in many control applications including controller design, realization theory, and model reduction. In this paper, we first propose an exact version alternating direction method for solving the nuclear norm minimization problem with linear equality constraints. At each iteration, the method involves a singular value thresholding and linear matrix equations which are solved exactly. Convergence of the proposed algorithm is followed directly. To broaden the capacity of solving larger problems, we solve approximately the subproblem by an iterative method with the Barzilai-Borwein steplength. Some extensions to the noisy problems and nuclear norm regularized least-square problems are also discussed. Numerical experiments and comparisons with the state-of-the-art method FPCA show that the proposed method is effective and promising. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Purpose: The goal of this paper is to extend our recently developed FBP (filtered backprojection) algorithm, which has the same characteristics of an iterative Landweber algorithm, to an FBP algorithm with the same characteristics of an iterative MAP (maximum a posteriori) algorithm. The newly developed FBP algorithm also works when the angular sampling interval is not uniform. The projection noise variance can be modeled using a view-based weighting scheme. Methods: The new objective function contains projection noise model dependent weighting factors and image dependent prior (i.e., a Bayesian term). The noise weighting is view-by-view based. For the first time, the FBP algorithm is able to model the projection noise. Based on the formulation of the iterative Landweber MAP algorithm, a frequency-domain window function is derived for each iteration of the Landweber MAP algorithm. As a result, the ramp filter and the windowing function are both modified by the Bayesian component. This new FBP algorithm can be applied to a projection data set that is not uniformly sampled. Results: Computer simulations show that the new FBP-MAP algorithm with window function index k and the iterative Landweber MAP algorithm with iteration number k give similar reconstructions in terms of resolution and noise texture. An example of transmission x-ray CT shows that the noise modeling method is able to significantly reduce the streaking artifacts associated with low-dose CT. Conclusions: View-based noise weighting scheme can be introduced to the FBP algorithm as a weighting factor in the window function. The new FBP algorithm is able to provide similar results to the iterative MAP algorithm if the ramp filter is modified with a additive term. Nonuniform sampling and sensitivity can be accommodated by proper backprojection weighting. [ABSTRACT FROM AUTHOR]

Higher order finite element discretizations, although providing higher accuracy, are considered to be computationally expensive and of limited use for large-scale problems. In this paper, we have developed an efficient iterative solver for solving large-scale quadratic finite element problems. The proposed approach shares some common features with geometric multigrid methods but does not need structured grids to create the coarse problem. This leads to a robust method applicable to finite element problems discretized by unstructured meshes such as those from adaptive remeshing strategies. The method is based on specific properties of hierarchical quadratic bases. It can be combined with an algebraic multigrid (AMG) preconditioner or with other algebraic multilevel block factorizations. The algorithm can be accelerated by flexible Krylov subspace methods. We present some numerical results on the convection-diffusion and linear elasticity problems to illustrate the efficiency and the robustness of the presented algorithm. In these experiments, the performance of the proposed method is compared with that of an AMG preconditioner and other iterative solvers. Our approach requires less computing time and less memory storage. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Multiuser orthogonal frequency division multiplexing (OFDM) is a promising technology to achieve high uplink/downlink (DL) capacities in the next generation broadband wireless networks such as WiMAX (Worldwide Interoperability for Microwave Access). In this paper, we investigate the DL adaptive power allocation (APA) in multiuser OFDM system from the perspective of cross-layer design. Specifically, we formulate APA as an optimization problem with the traffic profile of each user asit a priori knowledge. To solve the optimization problem, we develop a fairness-constrained optimal prioritized effective throughput (PET) strategy and the corresponding iterative algorithms, aiming at balancing the prioritized effective throughput and the linear or logarithmic user satisfaction-based fairness. Simulation results show that our proposed APA optimization approach can achieve satisfying performance. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Purpose: This paper studies the feasibility of developing an automatic anatomy segmentation (AAS) system in clinical radiology and demonstrates its operation on clinical 3D images.Methods: The AAS system, the authors are developing consists of two main parts: object recognition and object delineation. As for recognition, a hierarchical 3D scale-based multiobject method is used for the multiobject recognition task, which incorporates intensity weighted ball-scale (b-scale) information into the active shape model (ASM). For object delineation, an iterative graph-cut-ASM (IGCASM) algorithm is proposed, which effectively combines the rich statistical shape information embodied in ASM with the globally optimal delineation capability of the GC method. The presented IGCASM algorithm is a 3D generalization of the 2D GC-ASM method that they proposed previously in Chen et al. [Proc. SPIE, 7259, 72590C1-72590C-8 (2009)]. The proposed methods are tested on two datasets comprised of images obtained from 20 patients (10 male and 10 female) of clinical abdominal CT scans, and 11 foot magnetic resonance imaging (MRI) scans. The test is for four organs (liver, left and right kidneys, and spleen) segmentation, five foot bones (calcaneus, tibia, cuboid, talus, and navicular). The recognition and delineation accuracies were evaluated separately. The recognition accuracy was evaluated in terms of translation, rotation, and scale (size) error. The delineation accuracy was evaluated in terms of true and false positive volume fractions (TPVF, FPVF). The efficiency of the delineation method was also evaluated on an Intel Pentium IV PC with a 3.4 GHZ CPU machine.Results: The recognition accuracies in terms of translation, rotation, and scale error over all organs are about 8 mm, 10° and 0.03, and over all foot bones are about 3.5709 mm, 0.35° and 0.025, respectively. The accuracy of delineation over all organs for all subjects as expressed in TPVF and FPVF is 93.01% and 0.22%, and all foot bones for all subjects are 93.75% and 0.28%, respectively. While the delineations for the four organs can be accomplished quite rapidly with average of 78 s, the delineations for the five foot bones can be accomplished with average of 70 s.Conclusions: The experimental results showed the feasibility and efficacy of the proposed automatic anatomy segmentation system: (a) the incorporation of shape priors into the GC framework is feasible in 3D as demonstrated previously for 2D images; (b) our results in 3D confirm the accuracy behavior observed in 2D. The hybrid strategy IGCASM seems to be more robust and accurate than ASM and GC individually; and (c) delineations within body regions and foot bones of clinical importance can be accomplished quite rapidly within 1.5 min. [ABSTRACT FROM AUTHOR]

In this paper, we present a sparse linear discriminant analysis (LDA) algorithm for high-dimensional objects in subspaces. In high dimensional data, groups of objects often exist in subspaces rather than in the entire space. For example, in text data classification, groups of documents of different types are categorized by different subsets of terms. The terms for one group may not occur in the samples of other groups. In the new algorithm, we consider a LDA to calculate a weight for each dimension and use the weight values to identify the subsets of important dimensions in the discriminant vectors that categorize different groups. This is achieved by including the weight sparsity term in the objective function that is minimized in the LDA. We develop an iterative algorithm for computing such sparse and orthogonal vectors in the LDA. Experiments on real data sets have shown that the new algorithm can generate better classification results and identify relevant dimensions. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation-based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd-tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O( mlog n), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi-Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state-of-art approaches. [ABSTRACT FROM AUTHOR]

The authors describe a technique for selectively sharpening only edges that were blurred due to various causes without making interference factors such as random noise more conspicuous. The selective sharpening technique described in this paper is implemented as an iterative updating nonlinear algorithm obtained by discretizing a type of nonlinear reaction-diffusion time-evolution equations. The update terms of this algorithm consist of a quadratic nonlinear smoothing term, reaction term, and overshooting term. By performing quantitative evaluation experiments, the authors showed that the proposed technique has significantly better selective sharpness enhancement capabilities than existing sharpness enhancement techniques such as the peaking method. In addition, the authors introduced a processing parameter adaptive control method in the proposed technique and applied it to the suppression of breathing distortions in video sequences. Breathing distortions, which are video sequence distortions that often appear in old films, are time-varying blurring distortions that occur due to temporal variations of the focus. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(5): 33–47, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10086 [ABSTRACT FROM AUTHOR]

In this paper, we study a fully implicit parallel Newton–Krylov–Schwarz method (NKS) for solving the bidomain equations describing the electrical excitation process of the heart. NKS has been used successfully for many non-linear problems, but this is the first attempt to use this method for the bidomain model which consists of a system of time dependent partial differential equations of mixed type. Our experiments on parallel computers show that the method is scalable and robust with respect to many of the parameters in the bidomain model. In the outer layer of the algorithm, we use a non-linearly implicit backward Euler method to discretize the time derivative, and the resulting systems of large sparse non-linear equations are solved using an inexact Newton method. The Jacobian system required to solve in each Newton iteration is solved with a GMRES method preconditioned by a new component-wise restricted additive Schwarz preconditioner. The efficiency and robustness of the overall method depend heavily on what preconditioner we use. By comparing several preconditioners, we found our new restricted additive Schwarz method offers the best performance. Our parallel software is developed using the PETSc package of Argonne National Laboratory. Numerical results obtained on an IBM SP will be reported. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper extends the relationship between the author's operator trigonometry and convergence rates and other properties of important iterative methods. A new interesting trigonometric preconditioning lemma is given. The general relationship between domain decomposition methods and the operator trigonometry is established. A new basic conceptual link between sparse approximate inverse algorithms and the operator trigonometry is observed. A new underlying fundamental inherent trigonometry of the classical successive over-relaxation scheme is exposed. Some improved trigonometric interpretations of minimum residual schemes are mentioned. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Many problems in image restoration can be formulated as either an unconstrained non-linear minimization problem, usually with a Tikhonov-like regularization, where the regularization parameter has to be determined; or as a fully constrained problem, where an estimate of the noise level, either the variance or the signal-to-noise ratio, is available. The formulations are mathematically equivalent. However, in practice, it is much easier to develop algorithms for the unconstrained problem, and not always obvious how to adapt such methods to solve the corresponding constrained problem. In this paper, we present a new method which can make use of any existing convergent method for the unconstrained problem to solve the constrained one. The new method is based on a Newton iteration applied to an extended system of non-linear equations, which couples the constraint and the regularized problem, but it does not require knowledge of the Jacobian of the irregularity functional. The existing solver is only used as a black box solver, which for a fixed regularization parameter returns an improved solution to the unconstrained minimization problem given an initial guess. The new modular solver enables us to easily solve the constrained image restoration problem; the solver automatically identifies the regularization parameter, during the iterative solution process. We present some numerical results. The results indicate that even in the worst case the constrained solver requires only about twice as much work as the unconstrained one, and in some instances the constrained solver can be even faster. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dispersed generators (DGs) such as fuel cells and solar cells will be installed on the demand side of power systems. Such dispersed facilities can reduce distribution system loss by appropriate allocation. Planning and operation of distribution systems with the dispersed facilities have already been discussed. In this paper, the authors discuss the extent to which distribution system loss can be reduced if DGs are optimally allocated on the demand side of the distribution system. In order to determine the optimal allocation and size of DGs so as to minimize the distribution system loss, an algorithm based on tabu search is employed. The proposed algorithm consists of iterated nested use of the tabu search algorithm. Namely, in the proposed algorithm, in one computational iteration, after the location of the DG is temporarily determined by tabu search, the size of the DG is also determined by tabu search so as to minimize the distribution system loss for the temporarily determined allocation. Numerical simulations are carried out for two system models in order to examine the validity of the algorithm. © 2001 Scripta Technica, Electr Eng Jpn, 136(2): 1–8, 2001 [ABSTRACT FROM AUTHOR]

This paper introduces a new iterative algorithm for the estimation of the mixture transition distribution (MTD) model, which does not require the use of any specific external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results show that this new algorithm performs at least as well as or better than other methods. The choice of initial values is also discussed. The MTD model was designed for the modeling of high-order Markov chains and has already proved to be a useful tool for the analysis of different types of time series such as wind speeds and social relationships. In this paper, we also propose to use it for the modeling of one-dimensional spatial data. An application using a DNA sequence shows that this approach can lead to better results than the classical Potts model. [ABSTRACT FROM AUTHOR]

Recently the authors proposed a simultaneous iteration algorithm for the computation of the partial derivatives of repeated eigenvalues and the corresponding eigenvectors of matrices depending on several real variables. This paper analyses the properties of that algorithm and extends it in several ways. The previous requirement that the repeated eigenvalue be dominant is relaxed, and the new generalized algorithm given here allows the simultaneous treatment of simple and repeated eigenvalues. Methods for accelerating convergence are examined. Numerical results support our theoretical analysis. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes an optimal consensus model to derive weights for linguistic preference relations (LPRs). Two indexes, an individual-to-group consensus index ( ICI) and a collective consensus index ( CCI), are introduced. An iterative algorithm is presented to describe the consensus reaching process. By changing the weights and modifying a pair of individuals' comparison judgments-which have largest deviation value to the group judgments-the consensus reaching process can terminate, while both ICI and CCI are controlled with predefined thresholds. The algorithm aims to preserve the decision makers' original information as much as possible. The model and algorithm are then extended to handle the uncertain additive LPRs. Finally, two examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Learning from positive and unlabeled examples (PU learning) is a partially supervised classification that is frequently used in Web and text retrieval system. The merit of PU learning is that it can get good performance with less manual work. Motivated by transfer learning, this paper presents a novel method that transfers the 'outdated data' into the process of PU learning. We first propose a way to measure the strength of the features and select the strong features and the weak features according to the strength of the features. Then, we extract the reliable negative examples and the candidate negative examples using the strong and the weak features (Transfer-1DNF). Finally, we construct a classifier called weighted voting iterative support vector machine (SVM) that is made up of several subclassifiers by applying SVM iteratively, and each subclassifier is assigned a weight in each iteration. We conduct the experiments on two datasets: 20 Newsgroups and Reuters-21578, and compare our method with three baseline algorithms: positive example-based learning, weighted voting classifier and SVM. The results show that our proposed method Transfer-1DNF can extract more reliable negative examples with lower error rates, and our classifier outperforms the baseline algorithms. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The Jacobi-Davidson (JD) algorithm is considered one of the most efficient eigensolvers currently available for non-Hermitian problems. It can be viewed as a coupled inner-outer iteration, where the inner one expands the search subspace and the outer one reduces the eigenpair residual. One of the difficulties in the JD efficient use stems from the definition of the most appropriate inner tolerance, so as to avoid useless extra work and keep the number of outer iterations under control. To this aim, the use of an efficient preconditioner for the inner iterative solver is of paramount importance. The present paper describes a fresh implementation of the JD algorithm with controlled inner iterations and block factorized sparse approximate inverse preconditioning for non-Hermitian eigenproblems in a parallel computational environment. The algorithm performance is investigated by comparison with a freely available software package such as SLEPc. The results show that combining the inner tolerance control with an efficient preconditioning technique can allow for a significant improvement of the JD performance, preserving a good scalability. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with studying some of well-known iterative methods in their tensor forms to solve a Sylvester tensor equation. More precisely, the tensor form of the Arnoldi process and full orthogonalization method are derived by using a product between two tensors. Then tensor forms of the conjugate gradient and nested conjugate gradient algorithms are also presented. Rough estimation of the required number of operations for the tensor form of the Arnoldi process is obtained, which reveals the advantage of handling the algorithms based on tensor format over their classical forms in general. Some numerical experiments are examined, which confirm the feasibility and applicability of the proposed algorithms in practice. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Among numerous iterative methods for solving the minimal nonnegative solution of an M-matrix algebraic Riccati equation, the structure-preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank-one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank-one component can be accurately recovered. We then propose an efficient hybrid method, called the two-phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two-phase SDA saves those SDA iterative steps that previously have to have for the rank-one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two-phase SDA. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Large-scale engineering computing using the discontinuous deformation analysis (DDA) method is time-consuming, which hinders the application of the DDA method. The simulation result of a typical numerical example indicates that the linear equation solver is a key factor that affects the efficiency of the DDA method. In this paper, highly efficient algorithms for solving linear equations are investigated, and two modifications of the DDA programme are presented. The first modification is a linear equation solver with high efficiency. The block Jacobi (BJ) iterative method and the block conjugate gradient with Jacobi pre-processing (Jacobi-PCG) iterative method are introduced, and the key operations are detailed, including the matrix-vector product and the diagonal matrix inversion. Another modification consists of a parallel linear equation solver, which is separately constructed based on the multi-thread and CPU-GPU heterogeneous platforms with OpenMP and CUDA, respectively. The simulation results from several numerical examples using the modified DDA programme demonstrate that the Jacobi-PCG is a better iterative method for large-scale engineering computing and that adoptive parallel strategies can greatly enhance computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the resource allocation problem in a general network configuration is addressed. In particular, we will present a distributed solution algorithm in one the hand, followed by the exact set of equations that solves for ( p,1)-proportionally fair allocation in an attempt to express the network optimal rates in a closed form on the other hand. First, the problem is presented as an optimization model that maximizes the social utility of the network. A duality approach is used to solve the network model in a timely synchronized iterative manner. Next, the exact analytical variant of the model is presented showing its equivalence to the numerical solution. The analytical model relies on the pattern of bottlenecks inside the network, which can be found using a weighted progressive filling. Such a pattern will help in finding the exact analytical set of equations that solves for proportionally fair rates for any network configuration. Closed-form solutions are now computed for different networks including well-known configurations such as linear, grid, and cyclic networks. Different simulation experiments are conducted along with the solution of standard optimization solvers. The results of the simulation, the solvers, and the analytical solutions coincide and present the same allocation. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Purpose: The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. Methods: This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numerical simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. Results: The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. Conclusions: The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts. [ABSTRACT FROM AUTHOR]

The paper presents a review of active set (AS) algorithms that have been deployed for implementation of fast model predictive control (MPC). The main purpose of the survey is to identify the dominant features of the algorithms that contribute to fast execution of online MPC and to study their influence on the speed. The simulation study is conducted on two benchmark examples where the algorithms are analyzed in the number of iterations and in the workload per iteration. The obtained results suggest directions for potential improvement in the speed of existing AS algorithms. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT Wind power is becoming an increasingly important technology for electric power generation in many power systems around the world. A typical wind farm consists of a relatively large number of turbines under some form of decentralized control. In this context, a cyber-attack to wind power infrastructure may not only cause immediate physical damage to the facility in question, but may also threaten the stability of the power system in which this facility operates. In this paper, we present a novel distributed algorithm aimed at detecting cyber-attacks in a wind farm. The cyber-attacks considered take the form of adversarial manipulation of different turbine-specific control logic parameters. The proposed algorithm relies on the operational dynamics specific to wind farms namely that turbines that are relatively close are subject to similar wind patterns and hence must be in similar control 'states' most of the time. This can be seen as a 'wisdom of the crowd' effect: the 'true' state is the state of the majority of turbines in physical proximity when only a few have been compromised. In the proposed algorithm, each turbine in the farm periodically shares information regarding their own control 'state' with neighboring turbines through a dedicated wireless channel. We test the performance of the proposed algorithm in a simulation test-bed based on Denmark's Horns Rev wind farm. The results indicate that iterative reputation or trust re-allocation enables a distributed identification of affected turbines under a wide array of cyber-attack scenarios. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finding minimum-norm fixed point of nonexpansive mappings. We present two types of iteration methods (one is implicit, and the other is explicit). We establish strong convergence theorems for both methods. Some applications are given regarding convex optimization problems and split feasibility problems. These results improve some known results existing in the literatures. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the paper [1], a direct version of the classical Kaczmarz algorithm was proposed, which gives us in only one iteration a solution of an arbitrary consistent system of linear equations. Unfortunately, as any direct method applied to large sparse matrices, this algorithm is based on some modifications of the system matrix sparsity structure such that a big fill-in appears. In order to overcome this difficulty, in the present paper we propose a modified version of this direct Kaczmarz algorithm in which the transformations applied to the system matrix try to conserve the initial sparsity structure. This transformations are done via clustering using Jaccard and Hamming distances. The modified Kaczmarz algorithm is no more a direct method, but we obtain an acceleration of convergence with respect to the classical Kaczmarz algorithm. Numerical experiments which ilustrate the efficiency of our algorithm are also presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Fault current calculation in distribution systems faces the problem with participation of inverter-based distributed generation (IBDG). This paper analyzes the fault response of IBDG in order to model it under fault condition. An adaptive algorithm based on an iterative technique is then proposed to calculate the fault current in a system with the installation of IBDG. This algorithm is first validated by the conventional fault calculation technique in case of a system without IBDG. Then, a time-variant simulation is performed to validate the proposed algorithm for the system with IBDG. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

SUMMARY The choice of the preconditioner is a key factor to accelerate the convergence of eigensolvers for large-size sparse eigenproblems. Although incomplete factorizations with partial fill-in prove generally effective in sequential computations, the efficient preconditioning of parallel eigensolvers is still an open issue. The present paper describes the use of block factorized sparse approximate inverse (BFSAI) preconditioning for the parallel solution of large-size symmetric positive definite eigenproblems with both a simultaneous Rayleigh quotient minimization and the Jacobi-Davidson algorithm. BFSAI coupled with a block diagonal incomplete decomposition proves a robust and efficient parallel preconditioner in a number of test cases arising from the finite element discretization of 3D fluid-dynamical and mechanical engineering applications, outperforming FSAI even by a factor of 8 and exhibiting a satisfactory scalability. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY An iterative method for finding the largest eigenvalue of a nonnegative tensor was proposed by Ng, Qi, and Zhou in 2009. In this paper, we establish an explicit linear convergence rate of the Ng-Qi-Zhou method for essentially positive tensors. Numerical results are given to demonstrate linear convergence of the Ng-Qi-Zhou algorithm for essentially positive tensors. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a practical two-term acceleration algorithm is proposed, the interval of the parameter which guarantees the convergence of the acceleration algorithm is analyzed in detail. Further, the acceleration ratio of the new acceleration algorithm is obtained in advance. The new acceleration algorithm is less sensitive to the parameter than the Chebyshev semi-iterative method. Finally, some numerical examples show that the accelerated algorithm is effective. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]