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Structured backward error analysis for a class of block three-by-three saddle point problems

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Abstract

Recently, a number of efficient iteration methods for the solution of a special class of block 3 × 3 saddle point systems have been proposed by some authors. In order to easily evaluate the strong stability of these numerical algorithms and provide a practical and reliable termination criterion, in this paper, we perform the structured backward error analysis for this type of block 3 × 3 saddle point system and present an explicit and computable formula of the normwise structured backward error. Some numerical experiments are performed to demonstrate that our results can be used to easily test the stability of running algorithms, and the new stopping criterion based on the derived structured backward error is more suitable and efficient than the commonly used residue-based one.

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Acknowledgements

The authors would like to thank the editor and the reviewers for their valuable comments and helpful suggestions, which greatly improve the presentation of this paper.

Funding

This work was supported by the National Natural Science Foundation of China (12071196).

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Authors and Affiliations

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

    Peng Lv & Bing Zheng

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  1. Peng Lv
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  2. Bing Zheng
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Correspondence to Bing Zheng.

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Lv, P., Zheng, B. Structured backward error analysis for a class of block three-by-three saddle point problems. Numer Algor 90, 59–78 (2022). https://doi.org/10.1007/s11075-021-01179-6

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  • DOI: https://doi.org/10.1007/s11075-021-01179-6

Keywords

Mathematics Subject Classification (2010)