矩阵奇异值分解问题重分析的摄动法
Perturbation Method for Reanalysis of the Matrix Singular Value Decomposition
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摘要: 本文提出了一般实矩阵奇异值分解问题重分析的摄动法.这是一种简捷、高效的快速重分析方法,对于提高各种需要反复进行矩阵奇异值分解的迭代分析问题的计算效率具有较重要的实用价值.文中导出了奇异值和左、右奇异向量的直到二阶摄动量的渐近估计算式.文末指出了将这种振动分析方法直接推广到一般复矩阵情况的途径.Abstract: The perturbation method for the reanalysis of the singular value decomposition(SVD) of general real matrices is presented in this paper. This is a simple but efficient reanalysis technique for the SVD, which is of great worth to enhance computational efficiency of the iterative analysis problems that require matrix singular value decomposition repeatedly. The asymptotic estimate formulas for the singular values and the corresponding left and right singular vectors up to second-order perturbation components are derived. At the end of the paper the way to extend the perturbation method to the case of general complex matrices is advanced.
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Key words:
- matrix algebra /
- singular value decomposition /
- reanalysis /
- perturbation method
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[1] Forsythe,G,E et al.,《计算机数值计算方法》(计九三译),清华大学出版吐,北京(1987),253-307. [2] 蒋尔雄等,《线性代数》,人民教育出版社,北京(1978),468-473. [3] 孙继广,咤矩阵扰动分析乡,科学出版仕,北京(1987),14-16,134-136. [4] 胡海昌,《多自由度结构固有振动理论》,科学出版让,北京(1987),1-26. [5] 吕振华、冯振东、方传流,线性特征值问题在模态坐标系中的矩阵摄动法,振动工程学报,2,(2)(1989),59-94.
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