A minimal residual algorithm for the inconsistent matrix equation AXB + CYD = E over anti-symmetric matrices

Author

Fang, Ling ; Li, Can ; Li, Bo ; Fu, Shilu ; Xue, Ying

Author_Institution

Dept. of Found. Studies, Logistical Eng. Univ. of PLA, Chongqing, China

fYear

2010

fDate

17-19 Dec. 2010

Firstpage

43

Lastpage

47

Abstract

A minimal residual algorithm based on the idea of the classical CG method for the inconsistent matrix equation AXB + CYD = E is constructed in this paper. By this method, the minimum norm least squares solution for anti-symmetric matrices can be obtained within finite iteration steps by choosing a special kind of initial iteration matrix when the matrix equation AXB + CYD = E is not consistent and an error bound is given. Finally, an example verifies the efficiency of the algorithm.

Keywords

iterative methods; least squares approximations; matrix algebra; antisymmetric matrices; finite iteration steps; inconsistent matrix equation; initial iteration matrix; minimal residual algorithm; minimum norm least squares solution; Equations; Iterative methods; Mathematical model; Matrix decomposition; Minimization; Symmetric matrices; Anti-symmetric matrix; iterative method; the least squares solution; the minimum norm solution;

fLanguage

English

Publisher

ieee

Conference_Titel

Apperceiving Computing and Intelligence Analysis (ICACIA), 2010 International Conference on

Conference_Location

Chengdu

Print_ISBN

978-1-4244-8025-8

Type

conf

DOI

10.1109/ICACIA.2010.5709847

Filename

5709847