منابع مشابه
On the numerical solution of generalized Sylvester matrix equations
The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection metho...
متن کاملAccurate solutions of M-matrix Sylvester equations
This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Sylvester equation AX + XB = C by which we mean both A and B have positive diagonal entries and nonpositive off-diagonal entries and P = Im⊗A+B⊗ In is a nonsingular M -matrix, and C is entrywise nonnegative. It is proved that small relative perturbations to the e...
متن کاملA matrix LSQR algorithm for solving constrained linear operator equations
In this work, an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$ and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$ where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$, $mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$, $ma...
متن کاملKrylov Subspace Methods for Large-Scale Constrained Sylvester Equations
We consider the numerical approximation to the solution of the matrix equation A1X+XA2 −Y C = 0 in the unknown matrices X, Y , under the constraint XB = 0, with A1, A2 of large dimensions. We propose a new formulation of the problem that entails the numerical solution of an unconstrained Sylvester equation. The spectral properties of the resulting coefficient matrices call for appropriately des...
متن کاملon the numerical solution of generalized sylvester matrix equations
the global fom and gmres algorithms are among the effective methods to solve sylvester matrix equations. in this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two cg-type algorithms for solving generalized sylvester matrix equations. the proposed methods are iterative projection metho...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1992
ISSN: 0895-4798,1095-7162
DOI: 10.1137/0613002