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Backward Stability Analysis of Weighted Linear Least-Squares Problems

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Abstract

A provably backward stable algorithm for the solution of weighted linear least-squares problems with indefinite diagonal weighted matrices is presented. However, a similar algorithm is not necessarily backward stable, when the weighted matrices are generalized saddle-point matrices. Thus, conditions are derived under which the algorithm is provably backward stable.

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Acknowledgements

This research was supported by 973 Program (2013CB329404), NSFC (11301223, 61170309), Chinese Universities Specialized Research Fund for the Doctoral Program (20110185110020), GDNSF (S2012040007333), the Fundamental Research Funds for the Central Universities (21611375) and Special Funds for Discipline Construction of Jinan University.

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Authors and Affiliations

  1. Jinan University, Shenzhen, Guangdong, 518053, P.R. China

    Chi-Ye Wu

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, P.R. China

    Ting-Zhu Huang

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  1. Chi-Ye Wu
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  2. Ting-Zhu Huang
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Correspondence to Chi-Ye Wu.

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Communicated by Ilio Galligani.

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Wu, CY., Huang, TZ. Backward Stability Analysis of Weighted Linear Least-Squares Problems. J Optim Theory Appl 162, 303–312 (2014). https://doi.org/10.1007/s10957-013-0463-9

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  • DOI: https://doi.org/10.1007/s10957-013-0463-9

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