| 摘要: |
| 本文研究了Sylvester矩阵方程AXB+CXTD=E自反(或反自反)最佳逼近解.利用所提出的共轭方向法的迭代算法,获得了一个结果:不论矩阵方程AXB+CXTD=E是否相容,对于任给初始自反(或反自反)矩阵X1,在有限迭代步内,该算法都能够计算出该矩阵方程的自反(或反自反)最佳逼近解.最后,三个数值例子验证了该算法是有效性的. |
| 关键词: Sylvester矩阵方程 Kronecker积 共轭方向法 最佳逼近解 自反矩阵 |
| DOI： |
| 分类号:O241.5 |
| 基金项目:安徽高校省级自然科学基金资助(KJ2011B119) |
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| AN ITERATIVE ALGORITHM FOR THE REFLEXIVE OPTIMAL APPROXIMATION SOLUTION OF MATRIX EQUATIONS AXB + CXTD=E |
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YANG Jia-wen1, SUN He-ming2
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1.Department of Basic, Chuzhou Vocational and Technical College, Chuzhou 239000, China;2.College of Science, Hohai University, Nanjing 210098, China
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| Abstract: |
| In this paper, we study the optimal approximation solutin of the Sylvester matrix equations AXB + CXTD=E over reflexive (anti-reflexive) matrices. By using the proposed conjugate direction method, we get a result that whatever matrix equations AXB + CXTD=E are consistent or not, for arbitrary initial reflexive (anti-reflexive) matrix X1, the reflexive (anti-reflexive) optimal approximation solution can be obtained within finite iteration steps in the absence of round-off errors. The effectiveness of the proposed algorithm is verified by three numerical examples. |
| Key words: sylvester matrix equations Kronecker product conjugate direction method optimal approximation solution reflexive matrix |
