The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C. (3rd April 2017)

• Record Type: Journal Article
• Authors: Zhang, Xiaodan; Sheng, Xingping
• Other Names: Loiseau Jean Jacques Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2017(2017)
• Publication Date: 2017-04-03
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2017/1624969
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation A X + X B = C . By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (skew symmetric) solution under some appropriate assumptions when any initial symmetric (skew symmetric) matrix X 0 is taken. Finally, two numerical examples are given to illustrate that the introduced iterative algorithms are more efficient.