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H-matrices play an important role in applied sciences such as numerical analysis and optimization theory. An attractive question is to identify whether a given matrix is an H-matrix. In this paper, we propose a new iterative algorithm for identifying H-matrices. We show that the proposed algorithm has linear convergence and can determine the H-matrix characterization for any given matrix. Its performance is illustrated in a set of numerical tests. [ABSTRACT FROM AUTHOR]

Abstract: The existing algorithms for the minimum concave cost network flow problems mainly focus on the single-source problems. To handle both the single-source and the multiple-source problem in the same way, especially the problems with dense arcs, a deterministic annealing algorithm is proposed in this paper. The algorithm is derived from an application of the Lagrange and Hopfield-type barrier function. It consists of two major steps: one is to find a feasible descent direction by updating Lagrange multipliers with a globally convergent iterative procedure, which forms the major contribution of this paper, and the other is to generate a point in the feasible descent direction, which always automatically satisfies lower and upper bound constraints on variables provided that the step size is a number between zero and one. The algorithm is applicable to both the single-source and the multiple-source capacitated problem and is especially effective and efficient for the problems with dense arcs. Numerical results on 48 test problems show that the algorithm is effective and efficient. [Copyright &y& Elsevier]

This paper is concerned with the problem of blind separation of an instantaneous mixture of sources (BSS), which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise, these methods fail and others (higher order statistics, etc.) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources that have a probability density function with unbounded domain of definition is described; here, the algorithm does not lead directly to a separation state but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources. [ABSTRACT FROM AUTHOR]

In this paper we propose a regularization of general Tikhonov type for large-scale ill-posed problems. We introduce the projection method of iterative bidiagonalization and show that the regularization parameter can be chosen without prior knowledge of the noise variance by using the method of balancing principle. An algorithm implicate the efficient numerical realization of the new choice rule. Numerical experiments for severely ill-show benchmark inverse problems show that new method is effective compared with other criterions. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the problem to a discretized form, it is considered as a quasi-assignment problem and then an iterative method is applied to find an approximate solution for the discretized form of the integral equation. An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given. [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]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two iterative algorithms are proposed to solve the linear matrix equations . When the matrix equations are consistent, by the first algorithm, a solution can be obtained within finite iterative steps in the absence of roundoff-error for any initial value, furthermore, the minimum-norm solution can be got by choosing a special kind of initial matrix. Additionally, the unique optimal approximation solution to a given matrix can be derived by finding the minimum-norm solution of a new matrix equations . When the matrix equations are inconsistent, we present the second algorithm to find the least-squares solution with the minimum-norm. Finally, two numerical examples are tested by MATLAB, the results show that these iterative algorithms are efficient. [Copyright &y& Elsevier]

Abstract: A nonlinear iteration method for solving a class of two-dimensional nonlinear coupled systems of parabolic and hyperbolic equations is studied. A simple iterative finite difference scheme is designed; the calculation complexity is reduced by decoupling the nonlinear system, and the precision is assured by timely evaluation updating. A strict theoretical analysis is carried out as regards the convergence and approximation properties of the iterative scheme, and the related stability and approximation properties of the nonlinear fully implicit finite difference (FIFD) scheme. The iterative algorithm has a linear constringent ratio; its solution gives a second-order spatial approximation and first-order temporal approximation to the real solution. The corresponding nonlinear FIFD scheme is stable and gives the same order of approximation. Numerical tests verify the results of the theoretical analysis. The discrete functional analysis and inductive hypothesis reasoning techniques used in this paper are helpful for overcoming difficulties arising from the nonlinearity and coupling and lead to a related theoretical analysis for nonlinear FI schemes. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space. The analytical solution and approximate solution are represented in terms of series. For any initial function , we prove , , . Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective. [Copyright &y& Elsevier]

The restarted GMRES algorithm proposed by Saad and Schultz [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869] is one of the most popular iterative methods for the solution of large linear systems of equations Ax = b with a nonsymmetric and sparse matrix. This algorithm is particularly attractive when a good preconditioner is available. The present paper describes two new methods for determining preconditioners from spectral information gathered by the Arnoldi process during iterations by the restarted GMRES algorithm. These methods seek to determine an invariant subspace of the matrix A associated with eigenvalues close to the origin and to move these eigenvalues so that a higher rate of convergence of the iterative methods is achieved. [ABSTRACT FROM AUTHOR]