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Multiplicative perturbation bounds for weighted polar decomposition

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Abstract

In this paper, we obtain the multiplicative perturbation bounds for generalized nonnegative polar factor of weighted polar decomposition under the weighted unitarily invariant norm, weighed Frobenius norm and weighted spectral norm, respectively. More sharper bounds than the known ones are also obtained under certain condition. Moreover, new multiplicative perturbation bounds for weighted unitary polar factor are also given under the weighted unitarily invariant norm, which improve the existing multiplicative perturbation bounds.

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Acknowledgments

The work was supported by the National Natural Science Foundation of China (No.11171371 and No.11101195). The authors would like to thank the referees for their valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Xiaoli Hong, Lingsheng Meng & Bing Zheng

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  1. Xiaoli Hong
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  2. Lingsheng Meng
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  3. Bing Zheng
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Correspondence to Bing Zheng.

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Hong, X., Meng, L. & Zheng, B. Multiplicative perturbation bounds for weighted polar decomposition. Calcolo 51, 515–529 (2014). https://doi.org/10.1007/s10092-013-0099-z

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  • DOI: https://doi.org/10.1007/s10092-013-0099-z

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