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In this paper, a computationally efficient algorithm for Bayesian joint change point detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of change points (CPs) in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First, a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum a posteriori (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data, and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the maximization–maximization algorithm, which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov chain Monte Carlo algorithm. [ABSTRACT FROM AUTHOR]

A large number of free boundary problems can be formulated as linear-complementarity problems. In this paper, we propose an inexact alternating direction method of multipliers for solving linear complementarity problem arising from free boundary problems by using the special structure of these problems. The convergence of our proposed method is proved. Numerical results show that the proposed method is feasible and effective, and it is significantly faster than modified alternating direction implicit algorithm and many other methods, especially when dimension of the problem being solved is large. [ABSTRACT FROM AUTHOR]

In this paper, we propose two iterative algorithms for finding the minimum-norm solution of a split minimization problem. We prove strong convergence of the sequences generated by the proposed algorithms. The iterative schemes are proposed in such a way that the selection of the step-sizes does not need any prior information about the operator norm. We further give some examples to numerically verify the efficiency and implementation of our new methods and compare the two algorithms presented. Our results act as supplements to several recent important results in this area. [ABSTRACT FROM AUTHOR]

This paper deals with novel mathematical methods to locate the edges of heated planar objects employing simple photodiodes. Thereby, both the lateral edge position and the axial distance of the object can be determined. Furthermore, a method which allows the estimation of the rotation angle of the investigated object is discussed. In contrast to an infrared camera, photodiodes and the required electronic components are insensitive to mechanical vibrations commonly experienced in industrial fabrication processes. Nevertheless, the limited spatial resolution of such photodiode ensemble demands for a signal-processing-based resolution enhancement, which is presented in this paper. By means of simulation results, the efficiency of the novel methods is verified. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the order of convergence and the efficiency of four families of iterative methods using frozen divided differences. The first two families correspond to a generalization of the secant method and the implementation made by Schmidt and Schwetlick. The other two frozen schemes consist of a generalization of Kurchatov method and an improvement of this method applying the technique used by Schmidt and Schwetlick previously. An approximation of the local convergence order is generated by the examples, and it numerically confirms that the order of the methods is well deduced. Moreover, the computational efficiency indexes of the four algorithms are presented and computed in order to compare their efficiency. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Regularization methods for the solution of ill-posed inverse problems can be successfully applied if a right estimation of the regularization parameter is known. In this paper, we consider the L1-regularized image deblurring problem and evaluate its solution using the iterative forward–backward splitting method. Based on this approach, we propose a new adaptive rule for the estimation of the regularization parameter that, at each iteration, dynamically updates the parameter value, following the evolution of the objective functional. The iterative algorithm automatically stops, without requiring any assumption about the perturbation process, when the parameter has reached a seemingly near optimal value. In spite of the fact that the optimality of this value has not yet been theoretically proved, a large number of numerical experiments confirm that the proposed rule yields restoration results competitive with those of the best state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to find the efficient iterative methods for solving the general matrix equation A1X+ XA2+A3XH+XHA4=B (including Lyapunov and Sylvester matrix equations as special cases) with the unknown complex (reflexive) matrix X. Design/methodology/approach – By applying the principle of hierarchical identification and the Hermitian/skew-Hermitian splitting of the coefficient matrix quadruplet A1; A2; A3; A4 the authors propose a shift-splitting hierarchical identification (SSHI) method to solve the general linear matrix equation A1X+XA2+A3XH+XHA4=B. Also, the proposed algorithm is extended for finding the reflexive solution to this matrix equation. Findings – The authors propose two iterative methods for finding the solution and reflexive solution of the general linear matrix equation, respectively. The proposed algorithms have a simple, neat and elegant structure. The convergence analysis of the methods is also discussed. Some numerical results are given which illustrate the power and effectiveness of the proposed algorithms. Originality/value – So far, several methods have been presented and used for solving the matrix equations by using vec operator and Kronecker product, generalized inverse, generalized singular value decomposition (GSVD) and canonical correlation decomposition (CCD) of matrices. In several cases, it is difficult to find the solutions by using matrix decomposition and generalized inverse. Also vec operator and Kronecker product enlarge the size of the matrix greatly therefore the computations are very expensive in the process of finding solutions. To overcome these complications and drawbacks, by using the hierarchical identification principle and the Hermitian=skew-Hermitian splitting of the coefficient matrix quadruplet (A1; A2; A3; A4), the authors propose SSHI methods for solving the general matrix equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual Lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from the data. The numerical experiments performed on test problems show that the algorithm gives good results both in terms of precision and computational efficiency. [Copyright &y& Elsevier]

Abstract: In this paper, the issue of multi-degree reduction of Bézier curves with C 1 and G 2-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method. [Copyright &y& Elsevier]

The phase problem is a major challenge when using X-ray crystallography for structure determination. This is especially true when the objects studied are macromolecular crystals, which contain many atoms and diffract quite poorly. For this reason, conventional direct methods, which are very successful for small and medium-sized molecule crystals, generally fail with protein crystals that do not diffract to atomic resolution. In this paper, we review some of the iterative phase retrieval methods used in optics, and present our own results obtained while trying to extend these methods to the field of macromolecular crystallography. A binary constraint on density has been incorporated in a new iterative algorithm, as well as into an existing Difference Map, in order to attempt crystallographic phase retrieval. Another existing algorithm, Charge Flipping, has been modified to test a connectivity-based phasing approach. While the results on binary densities could not be extended to realistic cases, the connectivity criterion has shown to possess some phase extension power. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyse an algorithm based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of the algorithm is not trivial, due to the irregular convergence behaviour frequently displayed by Krylov subspace methods for nonsymmetric systems. Numerical experiments, carried out on several test problems, indicate that the more robust methods, such as GMRES and QMR, embedded in the adaptive enlargement scheme, exhibit good performances. [Copyright &y& Elsevier]

Abstract: The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficient solutions of coupled restricted singular matrix equations. Furthermore, the need to compute the weighted Drazin and weighted Moore–Penrose inverses; and the use of Tian''s work and Lev-Ari''s results are due to appearance in the solutions of these problems. The several special cases of these problems are also considered which includes the well-known coupled Sylvester matrix equations. Finally, we recover the iterative methods to the weighted case in order to obtain the minimum D-norm G-vector least-squares solutions for the coupled Sylvester matrix equations and the results lead to the least-squares solutions and invertible solutions, as a special case. [Copyright &y& Elsevier]

Many optimization problems reduce to the solution of a system of linear inequalities (SLI). Some solution methods use relaxed, averaged projections. Others invoke surrogate constraints (typically stemming from aggregation). This paper proposes a blend of these two approaches. A novelty comes from introducing as surrogate constraint a halfspace defined by differences of algorithmic iterates. The first iteration is identical to surrogate constraints methods. In next iterations, for a given approximation x¯, besides the violated constraints in x¯, we also take into consideration the surrogate inequality, which we have obtained in the previous iteration. The motivation for this research comes from the recent work of Scolnik et al. (Appl. Numer. Math. 41, 499—513, 2002), who studied some projection methods for a system of linear equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper extended algorithm of Karmarkar’s interior point algorithm is considered. Theoretical aspects of the new algorithm are discussed. We show that the new iterative algorithm converges faster than former Karmarkar’s algorithms. Successful convergence for problems of different sizes is obtained. Numerical results show that when we use a new parameter in the classical Karmarkar’s algorithm, number of iterations is less than the number of iterations for two mentioned methods. [Copyright &y& Elsevier]

With the ubiquity of large-scale computing resources has come significant attention to practical details of fast algorithms for the numerical solution of partial differential equations. Included in this group are the class of multigrid and algebraic multigrid algorithms that are effective solvers for many of the large matrix problems arising from the discretization of elliptic operators. Algebraic multigrid (AMG) is especially effective for many problems with discontinuous coefficients, discretized on unstructured grids, or over complex geometries. While much effort has been invested in improving the practical performance of AMG, little theoretical understanding of this performance has emerged. This paper presents a two-level convergence theory for a reduction-based variant of AMG, called AMGr, which is particularly appropriate for linear systems that have M-matrix-like properties. For situations where less is known about the problem matrix, an adaptive version of AMGr that automatically determines the form of the reduction needed by the AMGr process is proposed. The adaptive cycle is shown, in both theory and practice, to yield an effective AMGr algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a two-step algorithm for solving singular linear systems is presented. We compare this algorithm with a DGCR type algorithm [A. Sidi, A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular non-symmetric linear systems, Linear Algebra Appl. 298 (1999) 99–113] by numerical experiments. An error analysis is given. [Copyright &y& Elsevier]

Abstract: In this paper two algorithms for computing the principal square root of a centrosymmetric H-matrix with positive diagonal entries are proposed. It is showed that our algorithms ensure significant savings in computational costs, as compared to the case of an arbitrary H-matrix A with positive diagonal entries. [Copyright &y& Elsevier]

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES(m) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algoritfims for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one. [ABSTRACT FROM AUTHOR]

In this paper, DFOM algorithm is presented. We compare DGMRES algorithm with DFOM algorithm by numerical experiment. Error analysis for projection method is also given. [Copyright &y& Elsevier]

Our goal in this paper is to discuss various issues we have encountered in trying to find and implement efficient solvers for a boundary integral equation (BIE) formulation of an iterative method for solving a reconstruction problem. We survey some methods from numerical linear algebra, which are relevant for the solution of this class of inverse problems. We motivate the use of our constructing algorithm, discuss its implementation and mention the use of preconditioned Krylov methods. [Copyright &y& Elsevier]

The paper describes a domain decomposition strategy which allows high efficiency parallel simulations of turbomachinery flows. The implicit ADI parallel solver is based on the scalar approximate factorisation. The Navier-Stokes (NS) and turbulence model equations are discretised by centred finite differences. The results prove that the parallel calculations with domain decomposition, in which each sub-domain explicitly communicates with the adjacent ones at the end of each implicit iteration, may suffer from a considerable deterioration of the convergence rate. A simple sub-iterative domain recoupling strategy allows recovering the convergence rate of a single processor computation. The strategy is carefully analysed and optimised in terms of inter-processor data communication rate and algorithm memory requirements. The span-wise domain decomposition is particularly suited for turbomachinery flows and is applied to a radial impeller and to an axial turbine stator and stage to prove the validity and the accuracy of the proposed approach. The results indicate that the parallel recoupled algorithm usually reach efficiencies of 0.8, with peaks over 0.9 with up to 16 processors, thereby allowing a considerable speed-up of design and verification calculations. [ABSTRACT FROM AUTHOR]

In the convergence theory of multisplittings for symmetric positive definite (s.p.d.) matrices it is usually assumed that the weighting matrices are scalar matrices, i.e., multiples of the identity. In this paper, this restrictive condition is eliminated. In its place it is assumed that more than one (inner) iteration is performed in each processor (or block). The theory developed here is applied to nonstationary multisplittings for s.p.d. matrices, as well as to two-stage multisplittings for symmetric positive semidefinite matrices. [ABSTRACT FROM AUTHOR]

Given convex scattered data in R3 we consider the constrained interpolation problem of finding a smooth, minimal Lp-norm (1 < p < ∞) interpolation network that is convex along the edges of an associated triangulation. In previous work the problem has been reduced to the solution of a nonlinear system of equations. In this paper we formulate and analyse a Newton-type algorithm for solving the corresponding type of systems. The correctness of the application of the proposed method is proved and its superlinear (in some cases quadratic) convergence is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to derive new computable convergence bounds for GMRES. The new bounds depend on the initial guess and are thus conceptually different from standard “worst-case” bounds. Most importantly, approximations to the new bounds can be computed from information generated during the run of a certain GMRES implementation. The approximations allow predictions of how the algorithm will perform. Heuristics for such predictions are given. Numerical experiments illustrate the behavior of the new bounds as well as the use of the heuristics. [ABSTRACT FROM AUTHOR]