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New matrix iterative methods for constraint solutions of the matrix equation $AXB=C$. (English) Zbl 1206.65145
Summary: Two new matrix iterative methods are presented to solve the matrix equation $AXB=C$, the minimum residual problem $\min_{X\in\cal S}\|AXB-C\|$ and the matrix nearness problem $\min_{X\in S_E}\|X-X^*\|$, where $\cal S$ 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 [{\it Y.-B. Deng} et al., Numer. Linear Algebra Appl. 13, No. 10, 801--823 (2006; Zbl 1174.65382); {\it G.-X. Huang} et al., J. Comput. Appl. Math. 212, No. 2, 231--244 (2008; Zbl 1146.65036); the author, Appl. Math. Comput. 170, No. 1, 711--723 (2005; Zbl 1081.65039); and {\it Y. Lei} and {\it A. Liao}, Appl. Math. Comput. 188, No. 1, 499--513 (2007; Zbl 1131.65038)]. Paige’s algorithm is used as the frame method for deriving these matrix iterative methods. Numerical examples are used to illustrate the efficiency of these new methods.

MSC:
65F30Other matrix algorithms
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References:
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