| 求解一类矩阵方程最佳逼近解的算法 |
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| 引用本文： | 胡珊珊,孙合明,钟青. 求解一类矩阵方程最佳逼近解的算法[J]. 贵州大学学报(自然科学版), 2009, 26(6): 4-6,13 |
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| 作者姓名： | 胡珊珊 孙合明 钟青 |
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| 作者单位： | 河海大学,理学院,江苏,南京,210098;河海大学,理学院,江苏,南京,210098;河海大学,理学院,江苏,南京,210098 |
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| 摘 要： | 应用复合最速下降法,给出了在加权范数下求解矩阵方程AXB＋CYD=E的对称最佳逼近解的一种迭代算法。在有限的误差范围内,对任意初始矩阵X0、Y0,运用迭代算法,经过有限步可得到矩阵方程的最佳逼近解,并给出的数值例子证实了该算法的有效性。
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| 关 键 词： | 复合最速下降法 最佳逼近 矩阵方程 最小范数解 对称解 |
Algorithm for the Optimal Approximation Solution of the Matrix Equation |
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| HU Shan-shan,SUN He-ming,ZHONG Qing. Algorithm for the Optimal Approximation Solution of the Matrix Equation[J]. Journal of Guizhou University(Natural Science), 2009, 26(6): 4-6,13 |
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| Authors: | HU Shan-shan SUN He-ming ZHONG Qing |
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| Affiliation: | HU Shan-shan,SUN He-ming,ZHONG Qing(College of Science,Hohai University,Nanjing 210098,China) |
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| Abstract: | This paper gives an iterative algorithm to obtain the symmetric optimal approximation solution of matrix equation AXB ＋ CYD = E with weighted Frobenius norm by applying the hybrid steepest descent method . In the absence of round off errors, for any initial matrix X0, Y0, the optimal approximation solution can be obtained within finite iteration steps. In this paper, the numerical example verifies the feasibility of the algorithm. |
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| Keywords: | hybrid steepest descent method optimal approximation matrix equation least-norm solution symmetric solution |
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