矩阵奇异值分解问题重分析的直接摄动法

Direct Perturbation Method for Reanalysis of Matrix Singular Value Decomposition

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．

The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics,mechanics, control theory, engineering, etc.. An indirect perturbation method haspreviously been proposed by the auther in this journal, and now the direct perturbation method has also been presented in this paper. The second-order perturbation results of non-repeated singular values and the corresponding left and rightsingular vectors are obtained. The results can meet the general needs of mostproblems of various practical applications. A numerical example is presented todemonstrate the effectiveness of the direct perturbation method.