矩阵奇异值分解问题重分析的直接摄动法

基金项目: 国家自然科学基金

Direct Perturbation Method for Reanalysis of Matrix Singular Value Decomposition

摘要: 矩阵奇异值分解的摄动重分析技术具有广泛的应用前景,作者继在文[2]中提出了一种间接摄动分析方法之后,在本文中又进一步提出了直接摄动法,建立了一般实矩阵的非重奇异值及其左、古奇异向量的二阶摄动计算公式.这可满足大多数实际应用问题的一般需要.文中以算例说明了直接摄动法的有效性.
- 矩阵代数 /
- 奇异值分解 /
- 重分析 /
- 摄动法
Abstract: The perturbational reanalysis technique of matrix singular value decomposition isapplicable to many theoretical and practical problems in mathematics,mechanics,control theory,engineering,etc..An indirect perturbation method has previously beenproposed by,the author in this journal,and now the direct perturbation method hasalso been presented in this paper.The second-order perturbation results of nonrepeated singular values and the corresponding left and right singular vectors areobtained.The results can meet the general needs of most problems of various practicalapplications.A numerical example is presented to demonstrate the effectiveness of thedirect perturbation method.
- matrix algebra /
- singular value decomposition /
- reanalysis /
- perturbation method

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