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A note on unique solvability of the absolute value equation

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Abstract

In this note, we show that the singular value condition \(\sigma _{\max }(B) < \sigma _{\min }(A)\) leads to the unique solvability of the absolute value equation \(Ax + B|x| = b\) for any b. This result is superior to those appeared in previously published works by Rohn (Optim Lett 3:603–606, 2009).

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Acknowledgements

The authors would like to thank the anonymous referees for providing helpful suggestions, which greatly improved the paper. Funding was provided by National Natural Science Foundation of China (No. 11961082) and 17HASTIT012.

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  1. School of Mathematics, Yunnan Normal University, Kunming, 650500, Yunnan, People’s Republic of China

    Shi-Liang Wu & Cui-Xia Li

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  1. Shi-Liang Wu
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  2. Cui-Xia Li
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Correspondence to Shi-Liang Wu.

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Wu, SL., Li, CX. A note on unique solvability of the absolute value equation. Optim Lett 14, 1957–1960 (2020). https://doi.org/10.1007/s11590-019-01478-x

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  • DOI: https://doi.org/10.1007/s11590-019-01478-x

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