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In this paper, we present the block least squares method for solving nonsymmetric linear systems with multiple right-hand sides. This method is based on the block bidiagonalization. We first derive two algorithms by using two different convergence criteria. The first one is based on independently minimizing the 2-norm of each column of the residual matrix… (More)

In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A ∈ R n×n , B ∈ R s×s , X and C ∈ R n×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-Sylvester-Like(GFSL) and Global GMRES-Sylvester-Like(GGSL) algorithms,… (More)

One of the most important problem for solving the linear system Ax = b, by using the iterative methods, is to use a good stopping criterion and to determine the common significant digits between each corresponding components of computed solution and exact solution. In this paper, for a certain class of iterative methods, we propose a way to determine the… (More)

This paper presents a new version of the successive approximations method for solving Sylvester equations AX À XB = C, where A and B are symmetric negative and positive definite matrices, respectively. This method is based on the block GMRES-Sylvester method. We also discuss the convergence of the new method. Some numerical experiments for obtaining the… (More)

Keywords: Moore–Penrose Singular matrix Approximate inverse GMRES method Rectangular matrix Preconditioning a b s t r a c t In this paper, an iterative scheme is proposed to find the roots of a nonlinear equation. It is shown that this iterative method has fourth order convergence in the neighborhood of the root. Based on this iterative scheme, we propose… (More)

We study the CSCS method for large Hermitian positive definite Toeplitz linear systems, which first appears in Ng's paper published in Ng, 2003, and CSCS stands for circulant and skew circulant splitting of the coefficient matrix A. In this paper, we present a new iteration method for the numerical solution of Hermitian positive definite Toeplitz systems of… (More)