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Convergence of a Ulm-like method for square inverse singular value problems with multiple and zero singular values

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Abstract

An interesting problem was raised in Vong et al. (SIAM J. Matrix Anal. Appl. 32:412–429, 2011): whether the Ulm-like method and its convergence result can be extended to the cases of multiple and zero singular values. In this paper, we study the convergence of a Ulm-like method for solving the square inverse singular value problem with multiple and zero singular values. Under the nonsingularity assumption in terms of the relative generalized Jacobian matrices, a convergence analysis for the multiple and zero case is provided and the quadratical convergence property is proved. Moreover, numerical experiments are given in the last section to demonstrate our theoretic results.

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Acknowledgments

Weiping Shen is supported in part by the Zhejiang Provincial Natural Science Foundation of China (grant LY17A010006). Yaohua Hu is supported in part by the National Natural Science Foundation of China (11601343, 11601344) and Natural Science Foundation of Guangdong (2016A030310038). Chong Li is supported in part by the National Natural Science Foundation of China (grants 11571308) and the Zhejiang Provincial Natural Science Foundation of China (grant LY18A010004). Jen-Chih Yao is supported in part by the GrantMOSTMOST 106-2923-E-039-001-MY3.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Weiping Shen

  2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Yaohua Hu

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Chong Li

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

  5. Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

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  1. Weiping Shen
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  2. Yaohua Hu
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  3. Chong Li
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  4. Jen-Chih Yao
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Correspondence to Weiping Shen.

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Shen, W., Hu, Y., Li, C. et al. Convergence of a Ulm-like method for square inverse singular value problems with multiple and zero singular values. Numer Algor 79, 375–398 (2018). https://doi.org/10.1007/s11075-017-0442-6

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  • DOI: https://doi.org/10.1007/s11075-017-0442-6

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