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A note on unique solvability of the absolute value equation

  • Shi-Liang WuEmail author
  • Cui-Xia Li
Short Communication
  • 44 Downloads

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).

Keywords

Absolute value equation Unique solution Singular values 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsYunnan Normal UniversityKunmingPeople’s Republic of China

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