New matrix iterative methods for constraint solutions of the matrix equation AXB = C

作者：Peng, Zhen-yun^*

来源：Journal of Computational and Applied Mathematics, 2010, 235(3): 726-735.

DOI：10.1016/j.cam.2010.07.001

• Iterative algorithm
• Matrix equation
• Matrix nearness problem
• Minimum residual problem

In this paper, two new matrix iterative methods are presented to solve the matrix equation AXB = C, the minimum residual problem min(X is an element of Y) parallel to AXB - C parallel to and the matrix nearness problem min(X is an element of SE) parallel to X - X*parallel to, where Y is the set of constraint matrices, such as symmetric, symmetric R-symmetric and (R, S)-symmetric, and S(E) is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than the matrix iterative methods proposed in Deng et al. (2006)[13], Huang et al. (2008) [15], Peng (2005) [16] and Lei and Liao (2007)[17]. Paige's algorithms are used as the frame method for deriving these matrix iterative methods. Numerical examples are used to illustrate the efficiency of these new methods.

• 出版日期2010-12-1
• 单位桂林电子科技大学