Developing Bi-CG and Bi-CR methods to solve generalized Sylvester-transpose matrix equations

Authors:
Masoud Hajarian
Affiliations:
Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran 19839
Venue:
International Journal of Automation and Computing
Year:
2014

Citing 7
Cited 0

Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
On Iterative Solutions of General Coupled Matrix Equations

SIAM Journal on Control and Optimization
Solutions to generalized Sylvester matrix equation by Schur decomposition

International Journal of Systems Science
Weighted least squares solutions to general coupled Sylvester matrix equations

Journal of Computational and Applied Mathematics
An extension of the conjugate residual method to nonsymmetric linear systems

Journal of Computational and Applied Mathematics
Iterative solutions to matrix equations of the form AiXBi=Fi

Computers & Mathematics with Applications
A Hessenberg method for the numerical solutions to types of block Sylvester matrix equations

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

The bi-conjugate gradients (Bi-CG) and bi-conjugate residual (Bi-CR) methods are powerful tools for solving nonsymmetric linear systems Ax = b. By using Kronecker product and vectorization operator, this paper develops the Bi-CG and Bi-CR methods for the solution of the generalized Sylvester-transpose matrix equation Σi=1p (AiXBi + CiXTDi) = E (including Lyapunov, Sylvester and Sylvester-transpose matrix equations as special cases). Numerical results validate that the proposed algorithms are much more efficient than some existing algorithms.