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Many real-life problems using mathematical modeling can be reduced to scalar and system of nonlinear equations. In this paper, we develop a family of three-step sixth-order method for solving nonlinear equations by employing weight functions in the second and third step of the scheme. Furthermore, we extend this family to the multidimensional case preserving the same order of convergence. Moreover, we have made numerical comparisons with the efficient methods of this domain to verify the suitability of our method. [ABSTRACT FROM AUTHOR]

In the early seventies, Shelah proposed a model-theoretic construction, nowadays called "iteration". This construction is an infinite replication in a tree-like manner where every vertex possesses its own copy of the original structure. Stupp proved that the decidability of the monadic second-order (MSO) theory is transferred from the original structure onto the iterated one. In its extended version discovered by Muchnik and introduced by Semenov, the iteration became popular in computer science logic thanks to a paper by Walukiewicz. Compared to the basic iteration, Muchnik's iteration has an additional unary predicate which, in every copy, marks the vertex that is the clone of the possessor of the copy. A widely spread belief that this extension is crucial is formally confirmed in the paper. Two hierarchies of relational structures generated from finite structures by MSO interpretations and either Shelah-Stupp's iteration or Muchnik's iteration are compared. It turns out that the two hierarchies coincide at level 1. Every level of the latter hierarchy is closed under Shelah-Stupp's interation. In particular, the former hierarchy collapses at level 1. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new four-dimensional hyperchaotic system derived from the chaotic maps of Peter de Jong's simple attractor and the discrete iterative function. In this work, our main motivation is to explore a link that can be developed to generate hyperchaos from 2D chaotic system. An association between 2D system and a higher order one was not studied in the previous literature. In fact, in the literature, there is no two-dimensional systems from which we are able to associate a four-dimensional one. In this context, a special interest is reserved to Peter de Jong system due to its exceptional advantages such as hypersensitivity and velocity. The challenge in this paper is the development of a four-dimensional hyperchaotic system associated to the Peter de Jong one while conserving its important characteristics such as hypersensitivity, velocity and the lack of equilibrium. The system structure that we will detail is different from other hyperchaotic systems widely suggested in the literature. In fact, the proposed attractor does not display any equilibrium point. A mathematical study is carried out in order to obtain time plots, Lyapunov exponents spectrum and bifurcation diagram. Finally, we will prove the high sensitivity of this system relative to its initial condition by simulations and experimental observations. [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]

In this paper, we show that the failure of the unique branch hypothesis () for tame iteration trees implies that in some homogenous generic extension of there is a transitive model containing such that is regular. The results of this paper significantly extend earlier works from [Non-tame mice from tame failures of the unique branch bypothesis, Canadian J. Math. 66(4) (2014) 903-923; Core models with more Woodin cardinals, J. Symbolic Logic 67(3) (2002) 1197-1226] for tame trees. [ABSTRACT FROM AUTHOR]

This paper describes iterative methods for the high frequency electromagnetic analysis using the finite element method of Maxwell equations including displacement current. The conjugate orthogonal conjugate gradient method has been widely used to solve a complex symmetric system. However, the conventional method suffers from oscillating convergence histories in large-scale analysis. In this paper, to solve large-scale complex symmetric systems arising from the formulation of the E method, an iterative substructuring method like the minimal residual method is presented, and the performance of the convergence of the method is evaluated by numerical results. As the result, the proposed method shows a stable convergence behavior and a fast convergence rate compared to other iterative methods. [ABSTRACT FROM AUTHOR]

Recursion is one of the most difficult programming topics for students. In this paper, an instructional method is proposed to enhance students' understanding of recursion tracing. The proposal is based on the use of rules to translate linear recursion algorithms into equivalent, iterative ones. The paper has two main contributions: the instructional method itself, and its evaluation, which is based on previous works of other authors on mental models of recursion. As a result, an enhancement was measured in the viability of mental models exhibited by students (both for linear and multiple recursion), but no significant improvement was detected in their skills for designing recursive algorithms. Evidence was also obtained of the fact that many students with (relatively) viable mental models for linear recursion have unviable mental models for multiple recursion. Finally, it was noticed that many students adopt inaccurate mental models if those models are adequate to handle the given algorithm. [ABSTRACT FROM PUBLISHER]

Abstract To balance the load and to discourage the free-riding in peer-to-peer (P2P) networks, many incentive mechanisms and policies have been proposed in the recent years. Global peer ranking is one such mechanism. In this mechanism, peers are ranked based on a metric called contribution index. Contribution index is defined in such a manner that peers are motivated to share the resources in the network. Fairness in the terms of upload to download ratio in each peer can be achieved by this method. However, calculation of contribution index is not trivial. It is computed distributively and iteratively in the entire network and requires strict clock synchronization among the peers. A very small error in clock synchronization may lead to wrong results. Furthermore, iterative calculation requires a lot of message overhead and storage capacity, which makes its implementation more complex. In this paper, we propose a simple incentive mechanism based on the contributions of peers, which can balance the upload and download amount of resources in each peer. It does not require iterative calculation, therefore, can be implemented with lesser message overhead and storage capacity without requiring strict clock synchronization. This approach is efficient as there are very less rejections among the cooperative peers. It can be implemented in a truly distributed fashion with O (N) time complexity per peer. Highlights • We proposed some design rules for fairness and gave mathematical justification for it. • The stable marriage approach for the selection of peers for resource sharing is proposed. • Algorithms for implementation in distributed system are proposed. • Detailed simulation study has been conducted. [ABSTRACT FROM AUTHOR]

Standby redundancy has been extensively applied to critical engineering systems to enhance system reliability. Researches on reliability evaluation for standby systems focus more on systems with binary‐state elements. However, multi‐state elements with different performances have played a significant role in engineering systems. This paper presents an approach for reliability analysis of standby systems composed of multi‐state elements with constant state transition rates and absorbing failure states. The approach allows modelling different standby systems beyond cold, warm and hot ones by taking into account differences in possible maintenance of elements in standby and operation modes and dependence of elements' operational behavior on their initial state at the time of activation. An iterative algorithm for reliability evaluation based on element state probabilities is suggested. Illustrating examples of evaluating reliability of different types of homogeneous and heterogeneous standby systems are demonstrated. [ABSTRACT FROM AUTHOR]

The problem of poles assignment and robust poles assignment in linear discrete-time periodic (LDP) system via periodic state feedback is discussed in this paper. Based on a numerical solution to the periodic Sylvester matrix equation, an iterative algorithm of computing the periodic feedback gain can be obtained. By optimizing the free parameter matrix in the proposed algorithm, according to robustness principle, an algorithm on the minimum norm and robust poles assignment for the LDP systems is presented. Two numerical examples are worked out to illustrate the effect of the proposed approaches. [ABSTRACT FROM AUTHOR]

Abstract The solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications. In this paper we introduce new flexible and deflated variants of the shifted block GMRES method for this problem class. The proposed methods solve the whole sequence of linear systems simultaneously, detecting effectively the linear systems convergence and allowing the use of variable preconditioning which may be particularly useful in some applications. Numerical experiments are illustrated to show the overall significant robustness of the iterative method for solving general sparse multi-shifted and multiple right-hand-side systems, and in realistic PageRank calculations. To the best of our knowledge, this is the first Krylov subspace method that combines deflation techniques and variable preconditioning for solving sequences of multi-shifted linear systems with multiple right-hand sides simultaneously. [ABSTRACT FROM AUTHOR]

For large sparse saddle point problems, Cao et al. studied a modified generalized parameterized inexact Uzawa (MGPIU) method (see [Y. Cao, M.Q. Jiang, L.Q. Yao, New choices of preconditioning matrices for generalized inexact parameterized iterative methods, J. Comput. Appl. Math. 235 (1) (2010) 263-269]). For iterative methods of this type, the choice of the relaxation parameter is crucial for the methods to achieve their best performance. In this paper, for an example of 2D Stokes equations, we derive the optimal relaxation parameter for the continuous version of the MGPIU method, by minimizing the corresponding convergence factor that is obtained using Fourier analysis. In addition, we find that the MGPIU method is mesh parameter independent, however, it depends asymptotically linearly on the viscosity ν, which suggests that the numerical methods for Stokes equations should be investigated with the presence of the viscosity ν, though it can be scaled out from the equations in advance. We use numerical experiments to validate our theoretical findings. [ABSTRACT FROM AUTHOR]

The paper presents a mathematical model of an ideal filamentary coil with a finite number of turns, derived by means of the method called truncated region eigenfunction expansion (TREE). The proposed solution allows quick computation of the filamentary coil impedance as well as of the impedance changes caused by the presence of a two-layered conductive material. The final formulas were presented in the closed form and implemented in Matlab. The results were verified using the finite element method in the COMSOL Multiphysics package as well as by means of other mathematical models. In all cases they show a very good agreement. The obtained values of coil impedance changes were compared in terms of the time of reaching the final results. In the case of the most significant calculations, which consisted of many iterations, the proposed solution turned out to be by far the fastest one. [ABSTRACT FROM AUTHOR]

Inspired by the iterative nature of many discretization methods for continuous dynamical systems, connections between iterative numerical methods in numerical linear algebra and continuous dynamical systems have been studied since 1970s. For stationary iterative methods solving linear systems, Chu (1988, 2008) discussed a connection to continuous dynamical systems by using the explicit Euler method, however, further understanding of stationary iterative methods might be limited due to the use of the explicit Euler method. This paper presents a new connection, based on the so-called discrete gradient methods, between SOR-type methods and gradient systems. There, the key of the discussion is the equivalence between SOR-type methods and the discrete gradient methods applied to gradient systems. The discussion leads to new interpretations for SOR-type methods. For example, a new derivation of SOR-type methods is found, these methods monotonically decrease a certain quadratic function, and a new interpretation of the relaxation parameter is obtained. Besides, while studying the new connection, a new discrete gradient is also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the split feasibility problem in Banach spaces. By converting it to an equivalent null-point problem, we propose two iterative algorithms, which are new even in Hilbert spaces. The parameter in one algorithm is chosen in such a way that no priori knowledge of the operator norms is required. It is shown that these two algorithms are strongly convergent provided that the involved Banach spaces are smooth and uniformly convex. Finally, we conduct numerical experiments to support the validity of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently. [ABSTRACT FROM AUTHOR]

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditions. More precisely, it is demonstrated that the preconditioned Mixed-Type Splitting (MTS) iterative methods can surpass the preconditioned AOR iterative methods for an entirely general class of preconditioners handled by Wang and Song [J. Comput. Appl. Math. 226 (2009), no. 1, 114-124]. Finally some numerical results are elaborated which confirm the validity of the established results. [ABSTRACT FROM AUTHOR]

We construct a number system for representing numbers in [0, 1] that is based on iterations of an asymmetric tent map that incorporates the golden ratio. It is already known that in this system a number has a periodic representation if and only if it lies in . We investigate other aspects of this system such as non-uniquely representable numbers, an inherent semigroup structure, connections with Wythoff's game, related sequences of rational functions, and its connection with an iterative scheme reminiscent of paper folding analysis. Many details of the above-mentioned connections are conjectural. [ABSTRACT FROM AUTHOR]

Making predictions about environmental systems is a challenge due to the high level of uncertainty involved. In this paper we give a general formulation of prediction under uncertainty as a boundary problem. This leads to development of a methodology for making predictions under uncertainty, named Iterative Closed Question Modelling (ICQM). ICQM involves iteratively devising questions and testing the certainty of their answers by creating complete model scenarios (complete taken to include structure, parameters and inputs for each scenario instance). The model scenarios are categorised in terms of which answer they support, and whether they are plausible or not. Using a simple two-parameter flow duration curve model, the paper demonstrates the application of ICQM using eight alternative uncertainty analysis techniques. ICQM provides a useful and generic approach to making predictions under uncertainty, helps to understand how existing techniques address the boundary problem differently and promotes the development of new techniques. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and consider a new hybrid shrinking projection method for finding a common element of the set EP of solutions of a generalized equilibrium problem, the common fixed point set F of finite uniformly closed families of countable Bregman quasi-Lipschitz mappings in reflexive Banach spaces. It is proved that under appropriate conditions, the sequence generated by the hybrid shrinking projection method converges strongly to some point in $\mathit{EP} \cap F$. Relative examples are given. Strong convergence theorems are proved. The application for Bregman asymptotically quasi-nonexpansive mappings is also given. The main innovative points in this paper are as follows: (1) the notion of the uniformly closed family of countable Bregman quasi-Lipschitz mappings is presented and the useful conclusions are given; (2) the relative examples of the uniformly closed family of countable Bregman quasi-Lipschitz mappings are given in classical Banach spaces $l^{2}$ and $L^{2}$; (3) the application for Bregman asymptotically quasi-nonexpansive mappings is also given; (4) because the main theorems do not need the boundedness of the domain of mappings, so a corresponding technique for the proof is given. This new results improve and extend the previously known ones in the literature. [ABSTRACT FROM AUTHOR]

Discrete linear repetitive processes operate over a subset of the upper-right quadrant of the 2D plane. They arise in the modeling of physical processes and also the existing systems theory for them can be used to effect in solving control problems for other classes of systems, including iterative learning control design. This paper uses a form of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma to develop new linear matrix inequality (LMI) based stability conditions and control law design algorithms for the strong practical stability property. Relative to alternatives, the LMIs for stability have a simpler structure and it is not required to impose particular structures on the matrix variables. These properties are extended to control law design, including those where state vector access is not required. Illustrative numerical simulation examples conclude the paper. [ABSTRACT FROM AUTHOR]

In this paper, an iterative algorithm is proposed to retrieve the particle-size distributions via Fraunhofer diffraction. A dual integral inversion was proposed in our previous work, the inversion is robust and generates precise particle sizing, if the diffraction pattern can be accurately captured. In real applications, the pattern can only be partially detected, and the inversion fails to reconstruct the size distributions in detail. However, the results of the inversion can be used to produce an initial estimate. Then, a simulated diffraction pattern was generated from the estimated particle sizes. The deviation between the measured pattern and the simulated one was deduced to correct the results of particle sizing. The corrections can be achieved in an iterative approach, and the particle-size distribution was updated subsequently. The iteration stopped once the deviation was below the target value. Both simulation and experiment were conducted to validate the feasibility and effectiveness of the proposed algorithm. The results demonstrate that the size distribution from the proposed algorithm agrees well with the original phantoms for both noise-free and noise-contaminated data. [ABSTRACT FROM AUTHOR]

In this paper, we consider S-iteration to find fixed points of continuous mappings on an arbitrary interval. We give some necessary and sufficient conditions for the convergence of this iteration. Also, we proved that the rate of convergence of S-iteration is better than some other iterations for continuous and nondecreasing mappings. It is also noted that the method of proof of Lemma 3 using S-iteration is slightly different from that using the iteration schemes like Mann. [ABSTRACT FROM AUTHOR]

In this paper, a variational Bayesian (VB)-based iterative algorithm for ARX models with random missing outputs is proposed. The distributions of missing outputs can be estimated in the VB-E step, and the distributions of unknown parameters can be estimated in the VB-M step by the estimated missing outputs and the available outputs. Compared with the expectation-maximization-based iterative algorithm, this algorithm computes the latent variable and the parameter distributions at each iteration. Therefore, it is more accurate. The simulation results demonstrate the advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper the interval-valued delay fractional differential equations (IDFDEs) under the Caputo generalized Hukuhara differentiability are introduced. By establishing some necessary comparison results and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of extremal solutions for interval-valued delay fractional differential equations. Several examples are presented to illustrate the concepts and results. [ABSTRACT FROM AUTHOR]

Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations, blocking communication requests are avoided, which makes it hard to isolate and handle any global vector. While some termination protocols were proposed for asynchronous iterations, only very few of them are based on global residual computation and guarantee effective convergence. But the most effective and efficient existing solutions feature two reduction operations, which constitutes an important factor of termination delay. In this paper, we present new, non-intrusive, protocols to compute a residual error under asynchronous iterations, requiring only one reduction operation. Various communication models show that some heuristics can even be introduced and formally evaluated. Extensive experiments with up to 5,600 processor cores confirm the practical effectiveness and efficiency of our approach. [ABSTRACT FROM AUTHOR]

In this paper, an iterative method based on quasilinearization is presented to solve a class of two dimensional partial integro differential equations that arise in nuclear reactor models and population models. Two different approaches based on Haar and Legendre wavelets are studied to develop numerical methods. In the first approach, time domain is approximated with the help of forward finite difference approach. In the second approach, both time as well as space domains are approximated by wavelets. Appropriate examples are solved using these methods and the obtained results are compared with the methods available in the recent literature. [ABSTRACT FROM AUTHOR]

This paper involves developing new mathematical expressions to find reorder point and order quantity for inventory management policies that explicitly consider storage space capacity. Both continuous and periodic reviews, as well as backlogged and lost demand during stockout, are considered. With storage space capacity, when on-hand inventory exceeds the capacity, the over-ordering cost of storage at an external warehouse is charged on a per-unit-period basis. The objective is to minimize the total cost, consisting of ordering, shortage, holding, and over-ordering costs. Demand and lead time are stochastic and discrete in nature. Demand during varying lead time is modeled using an empirical distribution so that the findings are not subject to assumptions of demand and lead time probability distributions. Due to the complexity of the developed mathematical expressions, the problems are solved using an iterative method. The method is tested with problem instances that use real data from industry. Optimal solutions of the problem instance are determined by performing exhaustive search. The proposed method can effectively find optimal solutions for continuous review policies and near optimal solutions for periodic review policies. Fundamental insights about the inventory policies are reported from a comparison between continuous review and periodic review solutions, as well as a comparison between backlog and lost sales cases. [ABSTRACT FROM AUTHOR]

In this paper, a predictor corrector two-point block method is proposed to solve the well-know Blasius and Sakiadis flow numerically. The Blasius and Sakiadis flow will be modeled by a third order boundary value problem. The main motivation of this study is to provide a new method that can solve the higher order BVP directly without reducing it to a system of first order equation. Two approximate solutions will be obtained simultaneously in a single step by using predictor corrector two-point block method able to solve the third order boundary value problem directly. The proposed direct predictor corrector two-point block method will be adapted with multiple shooting techniques via a three-step iterative method. The advantage of the proposed code is that the multiple shooting will converge faster than the shooting method that has been implemented in other software. The developed code will automatically choose the guessing values in order to solve the given problems. Some numerical results are presented and a comparison to the existing methods has been included to show the performance of the proposed method for solving Blasius and Sakiadis flow. [ABSTRACT FROM AUTHOR]

In this paper, we considered a matrix inequality constrained linear matrix operator minimization problems with a particular structure, some of whose reduced versions can be applicable to image restoration. We present an efficient iteration method to solve this problem. The approach belongs to the category of Powell-Hestense-Rockafellar augmented Lagrangian method, and combines a nonmonotone projected gradient type method to minimize the augmented Lagrangian function at each iteration. Several propositions and one theorem on the convergence of the proposed algorithm were established. Numerical experiments are performed to illustrate the feasibility and efficiency of the proposed algorithm, including when the algorithm is tested with randomly generated data and on image restoration problems with some special symmetry pattern images. [ABSTRACT FROM AUTHOR]

In this paper, we prove a strong convergence theorem for finding a common element of the solution set of a constrained convex minimization problem and the set of solutions of a finite family of variational inclusion problems in Hilbert space. A strong convergence theorem for finding a common element of the solution set of a constrained convex minimization problem and the solution sets of a finite family of zero points of the maximal monotone operator problem in Hilbert space is also obtained. Using our main result, we have some additional results for various types of non-linear problems in Hilbert space. [ABSTRACT FROM AUTHOR]

An accurate model of the PV panel is useful to predict its behavior at all operating points for various applications. However, most of the manufacturers provide datasheet values at only open circuit point, short circuit point and maximum power point. Single mechanism five parameters (1M5P) model which contains a series and parallel resistance is presented. The model has five unknown parameters which need to be extracted. In this paper, the parameter extraction technique is improved for accuracy, simplicity and practicability. It requires minimum amount of data from the datasheet and does not require any complex iteration. The accuracy of the model with improved parameter extraction technique (IPET) is firstly validated with datasheet in the controlled irradiation environment. Secondly it is also compared under real-time uncontrolled irradiation environment in order to check the practicability of the model. Finally, the experiment for uncontrolled irradiation environment is carried out on three operating point’s i.e. maximum power point and two half power points to verify the accuracy of the model over the wider operating range.. The results of the model with IPET are in good agreement with both datasheet and experimental results with difference of less than 5%. It also shows significant improvement in accuracy when compared to the existing models. [ABSTRACT FROM AUTHOR]

In this paper, we first formulate a linear quasi-static poroelastic shell model of Naghdi's type. The model is given in three unknowns: displacement [ABSTRACT FROM AUTHOR]

Constructing a visual appearance model is essential for visual tracking. However, relying only on the visual model during appearance changes is insufficient and may even interfere with achieving good results. Although several visual tracking algorithms emphasize motional tracking that estimates the motion state of the object center between consecutive frames, they suffer from accumulated error during runtime. As neither visual nor motional trackers are capable of performing well separately, several groups have recently proposed simultaneous visual and motional tracking algorithms. However, because tracking problems are often NP-hard, these algorithms cannot provide good solutions for the reason that they are driven top-down with low flexibility and often encounter drift problems. This paper proposes a spiral visual and motional tracking (SVMT) algorithm which, unlike existing algorithms, builds a strong tracker by cyclically combining weak trackers from both the visual and motional layers. In the spiral-like framework, an iteration model is used to search for the optimum until convergence, with the potential for achieving optimization. Three learned procedures including visual classification, motional estimation, and risk analysis are integrated into the generalized framework and implement corresponding modifications with regard to their performances. The experimental results demonstrate that SVMT performs well in terms of accuracy and robustness. [ABSTRACT FROM AUTHOR]

The corrective calibration of the removal function plays an important role in the magnetorheological finishing (MRF) high-accuracy process. This paper mainly investigates the asymmetrical characteristic of the MRF removal function shape and further analyzes its influence on the surface residual error by means of an iteration algorithm and simulations. By comparing the ripple errors and convergence ratios based on the ideal MRF tool function and the deflected tool function, the mathematical models for calibrating the deviation of horizontal and flowing directions are presented. Meanwhile, revised mathematical models for the coordinate transformation of an MRF machine is also established. Furthermore, a Ø140-mm fused silica plane and a Ø196  mm, f/1∶1, fused silica concave sphere samples are taken as the experiments. After two runs, the plane mirror final surface error reaches PV 17.7 nm, RMS 1.75 nm, and the polishing time is 16 min in total; after three runs, the sphere mirror final surfer error reaches RMS 2.7 nm and the polishing time is 70 min in total. The convergence ratios are 96.2% and 93.5%, respectively. The spherical simulation error and the polishing result are almost consistent, which fully validate the efficiency and feasibility of the calibration method of MRF removal function error using for the high-accuracy subaperture optical manufacturing. [ABSTRACT FROM AUTHOR]

Purpose – Generally, iterative methods which have some instability solutions in complex structural and non-linear mechanical problems are used to compute reliability index. The purpose of this paper is to establish a non-linear conjugate gradient (NCG) optimization algorithm to overcome instability solution of the Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method in first-order reliability analysis. The NCG algorithms such as the Conjugate-Descent (CD) and the Liu-Storey (LS) are used for determining the safety index. An algorithm is found based on the new line search in the reliability analysis. Design/methodology/approach – In the proposed line search for calculating the safety index, search direction is computed by using the conjugate gradient approach and the HL-RF method based on the new and pervious gradient vector of the reliability function. A simple step size is presented for the line search in the proposed algorithm, which is formulated by the Wolfe conditions based on the new and previous safety index results in the reliability analysis. Findings – From the current work, it is concluded that the proposed NCG algorithm has more efficient, robust and appropriate convergence in comparison with the HL-RF method. The proposed methods can eliminate numerical instabilities of the HL-RF iterative algorithm in highly non-linear performance function and complicated structural limit state function. The NGC optimization is applicable to reliability analysis and it is correctly converged on the reliability index. In the NCG method, the CD algorithm is slightly more efficient than the LS algorithm. Originality/value – This paper usefully shows how the HL-RF algorithm and the NCG scheme are formulated in first-order reliability analysis. The proposed algorithm is validated from six numerical and structural examples taken from the literature. The HL-RF method is not converged on several non-linear mathematic and complex structural examples, while the two proposed conjugate gradient methods are appropriately converged for all examples. The CD algorithm is converged about twice faster than the LS algorithm in most of the problems. Therefore, application of the NCG method is possible in reliability analysis. [ABSTRACT FROM AUTHOR]

Abstract: FE model updating techniques are used to update dynamic FE models of structures in the light of modal test data. Iterative methods of model updating that update a set of chosen parameters of the model, so as to reduce the difference between the natural frequencies and the mode shapes of the FE model and the corresponding quantities obtained through a modal test on the structure, are probably the most widely used methods. Once experimental modal data has been identified, a necessary prior step, before updating can be carried out, is that of establishing the correspondence between the FE model modes and the experimentally identified modes. It is however experienced that, many a times a situation is encountered where not all of the modes identified through an experiment can be correlated with certainty with those predicted by the FE model and some experimental modes may be left uncorrelated. There could be several reasons for this lack of correlation as identified in the paper. But the consequence is that such uncorrelated modes cannot be used in FE model updating using existing iterative methods based on modal data even when they form valid known pieces of information about the structure. This is a disadvantage since it reduces the quantity of experimental data available for model updating and hence makes the updating process less effective in yielding an updated model that is a closer representation of the structure. This paper identifies this as a limitation of the existing iterative methods of model updating based on modal data and puts forward a notion of FE model updating using uncorrelated modes. The paper proposes a solution to overcome this limitation in the form of a new method of FE model updating that accepts both correlated as well as uncorrelated modes for updating. This is in contrast to all the current iterative modal data based methods of model updating that are based on the assumption of availability of correlated mode pairs and hence cannot use uncorrelated mode shapes and corresponding natural frequencies in the updating process. Formulation of the proposed method is described followed by a couple of numerical examples based on a beam structure to validate the method. The robustness of the method in the presence of simulated noise is also studied. Another numerical example of a more complex F-shape structure is also presented. The method is then validated though an experimental study. The proposed method is found to successfully update an FE model yielding correct estimates of the updating parameters in the presence of uncorrelated modes. [Copyright &y& Elsevier]

This paper develops a generalized admittance matrix approach in Fortescue coordinate system to solve unbalanced/unsymmetrical distribution networks including different number of phases. This generalized Fortescue \pi equivalent is defined in this paper for solving the heterogeneous phase, and thus Fortescue, network model. The performance of the approach is demonstrated in different model networks with number of nodes ranging between 168 and 14200. It is found that the current iteration method exploiting the decoupling in admittance matrix in Fortescue coordinate is substantially faster than the typical unbalanced three-phase solution in phase domain. The method has a significant potential for application in real time active power network management. [ABSTRACT FROM PUBLISHER]

This paper introduces and analyzes a viscosity iterative algorithm for an infinite family of nonexpansive mappings {...} in the framework of a strictly convex and uniformly smooth Banach space. It is shown that the proposed iterative method converges strongly to a common fixed point of {...}, which solves specific variational inequalities. Necessary and sufficient convergence conditions of the iterative algorithm for an infinite family of nonexpansive mappings are given. Results shown in this paper represent an extension and refinement of the previously known results in this area. [ABSTRACT FROM AUTHOR]

The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption distribution is supposed to be a perturbation of a piecewise constant function. Analyzing the acousto-optic measurements, we prove that the optical absorption coefficient satisfies, in the sense of distributions, a new equation. For doing so, we introduce a weak Helmholtz decomposition and interpret in a weak sense the cross-correlation measurements using the spherical Radon transform. We next show how to find an initial guess for the unknown coefficient. Finally, in order to construct the true coefficient we provide a Landweber type iteration and prove that the resulting sequence converges to the solution of the system constituted by the optical diffusion equation and the new equation mentioned above. Our results in this paper generalize the acousto-optic process proposed in [5] for piecewise smooth optical absorption distributions. [ABSTRACT FROM AUTHOR]

The paper presents a new model of the STATCOM aimed at power flow solutions using the Newton–Raphson method. The STATCOM is made up of the series connection of a voltage-source converter (VSC) and its connecting transformer. The VSC is represented in this paper by a complex tap-changing transformer whose primary and secondary windings correspond, notionally speaking, to the VSC's ac and dc buses, respectively. The magnitude and phase angle of the complex tap changer are said to be the amplitude modulation index and the phase shift that would exist in a PWM inverter to enable either reactive power generation or absorption purely by electronic processing of the voltage and current waveforms within the VSC. The new STATCOM model allows for a comprehensive representation of its ac and dc circuits—this is in contrast to current practice where the STATCOM is represented by an equivalent variable voltage source, which is not amenable to a proper representation of the STATCOM's dc circuit. One key characteristic of the new VSC model is that no special provisions within a conventional ac power flow solution algorithm is required to represent the dc circuit, since the complex tap-changing transformer of the VSC gives rise to the customary ac circuit and a notional dc circuit. The latter includes the dc capacitor, which in steady-state draws no current, and a current-dependent conductance to represent switching losses. The ensuing STATCOM model possesses unparalleled control capabilities in the operational parameters of both the ac and dc sides of the converter. The prowess of the new STATCOM power flow model is demonstrated by numerical examples where the quadratic convergence characteristics of the Newton–Raphson method are preserved. [ABSTRACT FROM PUBLISHER]

This paper studies the solution of both asymmetric and symmetric linear complementarity problems by two-phase methods that consist of an active set prediction phase and an acceleration phase. The prediction phase employs matrix splitting iterations that are tailored to the structure of the linear complementarity problems studied in this paper. In the asymmetric case, the task of pairing an acceleration phase with matrix splitting iterations is achieved by exploiting a contraction property associated with certain matrix splittings. For symmetric problems, a similar task is achieved by utilizing decent properties of specific matrix splitting iterations and projected searches. The superior optimal active set identification property of matrix splitting iterations is illustrated with numerical experiments, which also demonstrate the general efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates agent search for the agent with the best value in a multi-agent system, according to some value assignment. In the type of setting considered, agent values are independent of one another. Under this condition, classic state-space search methods are not very suitable solutions since they must probe the values of all agents in order to determine who the best-valued agent is. The method considered in this paper refines the number of agents that need to be probed by iteratively publishing thresholds on acceptable agent values. This kind of agent search is applicable to various domains, including auctions, first responders, and sensor networks. In the model considered, there is a fixed cost for publishing the thresholds and a variable cost for obtaining agent values that increases with the number of values obtained. By transforming the threshold-based sequence to a probability-based one, the sequence with minimum expected cost is proven to consist of either a single search round or an infinite sequence of increasing thresholds. This leads to a simplified characterization of the optimal thresholds sequence from which the sequence can be derived. The analysis is extended to the case of search for multiple agents. One important implication of this method is that it improves the performance of legacy economic-search methods that are commonly used in “search theory”. Within this context, we show how a threshold-based search can be used to augment existing economic search techniques or as an economic search technique itself. The effectiveness of the methods for both best-value search and economic-search is demonstrated numerically using a synthetic environment. [Copyright &y& Elsevier]

This paper suggests a data envelopment analysis (DEA) model for selecting the most efficient alternative in advanced manufacturing technology in the presence of both cardinal and ordinal data. The paper explains the problem of using an iterative method for finding the most efficient alternative and proposes a new DEA model without the need of solving a series of LPs. A numerical example illustrates the model, and an application in technology selection with multi-inputs/multi-outputs shows the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper we introduce two strategies for picking relaxation parameters to control the semiconvergence behavior of a sequential block-iterative method. A convergence analysis is presented. We also demonstrate the performance of our strategies by examples taken from tomographic imaging. [ABSTRACT FROM AUTHOR]

Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac conductivities in models of potential propagation is crucial, since they have major quantitative impact on the solution. Available estimates of cardiac conductivities are significantly diverse in the literature and the definition of experimental/mathematical estimation techniques is an open problem with important practical implications in clinics. We have recently proposed a methodology based on a variational procedure, where the reliability is confirmed by numerical experiments. In this paper we explore model-order-reduction techniques to fit the estimation procedure into timelines of clinical interest. Specifically we consider the Monodomain model and resort to Proper Orthogonal Decomposition (POD) techniques to take advantage of an offline step when solving iteratively the electrocardiological forward model online. In addition, we perform the Discrete Empirical Interpolation Method (DEIM) to tackle the nonlinearity of the model. While standard POD techniques usually fail in this kind of problems, due to the wave-front propagation dynamics, an educated novel sampling of the parameter space based on the concept of Domain of Effectiveness introduced here dramatically reduces the computational cost of the inverse solver by at least 95%. [ABSTRACT FROM AUTHOR]

Data clustering is a necessary process in many scientific disciplines, and fuzzy c-means (FCM) is one of the most popular clustering algorithms. Recently, distributing weight values and avoiding local minimization are the possible ways to improve the results of FCM. In this paper, fuzzy C-means clustering based on weights and gene expression programming (WGFCM) is proposed to improve the performance of FCM. A new weight vectors calculation based on entropy is introduced to measure distance accurately. Moreover, gene expression programming (GEP) is employed to determine the appropriate cluster centers. Experiments are conducted with ten UCI data sets to compare the proposed method with FCM. In addition, WGFCM is compared with other FCM based methods and different clustering approaches published for a fair assessment. The results show that the proposed method is far superior to FCM-based methods in terms of purity, Rand Index, accuracy rate, objective function value and iterative cost. Moreover, it has an advantage over other clustering approaches in terms of the accuracy. [ABSTRACT FROM AUTHOR]

This paper establishes existence of optimal controls for a general stochastic impulse control problem. For this, the value function is characterized as the pointwise minimum of a set of superharmonic functions, as the unique continuous viscosity solution of the quasi-variational inequalities (QVIs), and as the limit of a sequence of iterated optimal stopping problems. A combination of these characterizations is used to construct optimal controls without relying on any regularity of the value function beyond continuity. Our approach is based on the stochastic Perron method and the assumption that the associated QVIs satisfy a comparison principle. [ABSTRACT FROM AUTHOR]

In this paper, a recently new semi-analytical method, i.e., He’s variational iteration method is developed to apply to free vibration analysis of conveying fluid pipe. The critical flow velocity and frequency of pipe conveying fluid are obtained with considering the various boundary conditions. The results are compared with the ones of different transform method, and prove VIM that has the same precision and efficient with DTM. The mode shapes of cantilevered pipe and both ends with elastic support pipe are shown under different flow velocity. [ABSTRACT FROM AUTHOR]

With the development of ultra-high-resolution display devices, the visual perception of fine texture details is becoming increasingly important. Traditional image upsampling methods suffer from either loss of high-frequency texture details or very high time cost. In this paper, we propose an iterative projection reconstruction (IPR) method for fast and efficient image upsampling. The proposed method refines high-frequency texture details with an iterative projection process, and utilizes the pre-computed projection matrix to accelerate the example-based image reconstruction. As a result, the proposed method can reproduce fine texture details with low time cost. Experimental results demonstrate that the proposed method outperforms some state-of-the-art methods. [ABSTRACT FROM AUTHOR]