Faezeh Toutounian

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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)
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)
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)
We present a nested splitting conjugate gradient iteration method for solving large sparse continuous Sylvester equation, in which both coefficient matrices are (non-Hermitian) positive semi-definite, and at least one of them is positive definite. This method is actually inner/outer iterations, which employs the Sylvester conjugate gradient method as inner(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)
In this paper, we propose a new method for solving general linear systems with several right-hand sides. This method is based on global least squares method and reduces the original matrix to the lower bidiagonal form. We derive a simple recurrence formula for generating the sequence of approximate solutions {X k }. Some theoretical properties of the new(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)