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Direct perturbation method for reanalysis of matrix singular value decomposition

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Abstract

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 has previously been proposed by the author 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 right singular vectors are obtained. The results can meet the general needs of most problems of various practical applications. A numerical example is presented to demonstrate the effectiveness of the direct perturbation method.

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Authors and Affiliations

  1. Qinghua University, 100084, Beijing, PR China

    Lü Zhenhua

Authors
  1. Lü Zhenhua
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Communicated by Sun Huanchun

Project supported by the National Natural Science Foundation of China

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Zhenhua, L. Direct perturbation method for reanalysis of matrix singular value decomposition. Appl Math Mech 18, 471–477 (1997). https://doi.org/10.1007/BF02453742

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  • DOI: https://doi.org/10.1007/BF02453742

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