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On estimating the separation associated with the periodic continuous Sylvester equation

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Abstract

The sensitivity of the solution of the periodic continuous Sylvester equation AkXk Dk − BkXk⊕1Ck = Ek, k = 0,1,…,K − 1, depends on the separation of two periodic matrix pairs \(\{(A_{k}, B_{k})\}_{k=0}^{K-1}\) and \(\{(C_{k},D_{k})\}_{k=0}^{K-1}\). In this paper, we derive upper and lower bounds of this separation in terms of periodic generalized Schur decompositions. The theoretical results are verified by a numerical example.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments, which help us to improve this paper.

Funding

This work is supported by the National Natural Science Foundations of China (11771159, 12171168, U1811464) and Guangdong Provincial Natural Science Foundation (2021A1515012032).

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  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Qingmin Yang & Xiao Shan Chen

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  1. Qingmin Yang
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  2. Xiao Shan Chen
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Correspondence to Xiao Shan Chen.

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Yang, Q., Chen, X.S. On estimating the separation associated with the periodic continuous Sylvester equation. Numer Algor 90, 1419–1435 (2022). https://doi.org/10.1007/s11075-021-01235-1

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