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The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint

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Abstract

In this paper, we present an iterative method for finding the least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. We prove that if the constrained matrix equations are consistent, the solution can be obtained within finite iterative steps in the absence of round-off errors; if constrained matrix equations are inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Finally, numerical examples are provided to illustrate the efficiency of the proposed method and testify the conclusions suggested in this paper.

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Acknowledgements

The authors deeply thank the anonymous referees for helping to improve the original manuscript by valuable suggestions.

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  1. College of Mathematics and Informatics, Fujian Key Laboratory of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Baohua Huang & Changfeng Ma

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  1. Baohua Huang
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  2. Changfeng Ma
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Correspondence to Changfeng Ma.

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Supported by National Science Foundation of China (41725017), National Basic Research Program of China under Grant No. 2014CB845906. It is also partially supported by the CAS/CAFEA international partnership Program for creative research teams (Nos. KZZD-EW-TZ-19, KZZD-EW-TZ-15), Strategic Priority Research Program of the Chinese Academy of Sciences (XDB18010202).

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Huang, B., Ma, C. The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. J Glob Optim 73, 193–221 (2019). https://doi.org/10.1007/s10898-018-0692-4

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