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| 摘要: |
| 本文研究了Sylvester复矩阵方程A1Z+ZB1=C1的广义自反最佳逼近解.利用复合最速下降法,提出了一种的迭代算法.不论矩阵方程A1Z+ZB1=C1是否相容,对于任给初始广义自反矩阵Z0,该算法都可以计算出其广义自反的最佳逼近解.最后,通过两个数值例子,验证了该算法的可行性. |
| 关键词: Sylvester矩阵方程 Kronecker积 复合最速下降法 最佳逼近 广义自反矩阵 |
| DOI： |
| 分类号:O241.6 |
| 基金项目:安徽省教育厅自然科学基金资助(KJ2011B119). |
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| AN ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE OPTIMAL APPROXIMATION SOLUTIONS OF MATRIX EQUATIONS A1Z+ZB1=C1 |
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YANG Jia-wen,SUN He-ming
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| Abstract: |
| In this paper, we present an iterative algorithm to calculate the optimal approximation solutions of the Sylvester complex matrix equations A1Z+ZB1=C1 over generalized reflexive (anti-reflexive) matrices by using the hybrid steepest descent method. Whether matrix equations A1Z+ZB1=C1 are consistent or not, for arbitrary initial reflexive (anti-reflexive) matrix Z0, the given algorithm can be used to compute the reflexive (anti-reflexive) optimal approximation solutions. The effectiveness of the proposed algorithm is verified by two numerical examples. |
| Key words: Sylvester matrix equations Kronecker product hybrid steepest descent method optimal approximation reflexive matrix |
