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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)

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, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a preconditioner for solving symmetric positive definite linear systems of equations by using the preconditioned conjugate… (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)

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)

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)