An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation

✍ Scribed by Guang-Xin Huang; Feng Yin; Ke Guo

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 174 KB
• Volume: 212
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2006.12.005

✦ Synopsis

In this paper, an iterative method is constructed to solve the linear matrix equation AXB = C over skew-symmetric matrix X. By the iterative method, the solvability of the equation AXB = C over skew-symmetric matrix can be determined automatically. When the equation AXB = C is consistent over skew-symmetric matrix X, for any skew-symmetric initial iterative matrix X 1 , the skew-symmetric solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique least-norm skew-symmetric iterative solution of AXB = C can be derived when an appropriate initial iterative matrix is chosen. A sufficient and necessary condition for whether the equation AXB = C is inconsistent is given. Furthermore, the optimal approximate solution of AXB = C for a given matrix X 0 can be derived by finding the least-norm skew-symmetric solution of a new corresponding matrix equation A XB = C. Finally, several numerical examples are given to illustrate that our iterative method is effective.