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Lopsided DSS iteration method for solving complex Sylvester matrix equation

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Abstract

In this study, based on the double-step scale splitting (DSS) iteration method for solving complex Sylvester matrix equation, we propose two corresponding lopsided DSS iteration methods. These new methods, LDSS1 and LDSS2, are proved to be convergent under some suitable conditions. Besides, we try to minimize the spectral radii of the iteration matrices. We compare the new methods to the original methods in terms of the spectral radii of the iteration matrices. In the experiment results, we found that LDSS1 and LDSS2 methods are superior in iteration steps and CPU time when Sylvester equation satisfies some certain conditions.

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Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11771393, 11632015).

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Authors and Affiliations

  1. School of Mathematical Science, Zhejiang University, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Yu-Ye Feng, Qing-Biao Wu & Zhe-Wei Xie

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  1. Yu-Ye Feng
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  2. Qing-Biao Wu
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  3. Zhe-Wei Xie
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Correspondence to Qing-Biao Wu.

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Communicated by Zhong-Zhi Bai.

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Feng, YY., Wu, QB. & Xie, ZW. Lopsided DSS iteration method for solving complex Sylvester matrix equation. Comp. Appl. Math. 40, 235 (2021). https://doi.org/10.1007/s40314-021-01628-x

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