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Numerical validation for systems of absolute value equations

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Abstract

This paper establishes a numerical validation test for solutions of systems of absolute value equations based on the Poincaré–Miranda theorem. In this paper, the Moore–Kioustelidis theorem is generalized for nondifferential systems of absolute value equations. Numerical results are reported to show the efficiency of the new test method.

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Acknowledgments

The authors thank the referee for his/her valuable comments and suggestions which improved the original manuscript of this paper.

Author information

Correspondence to H. J. Wang or H. Liu.

Additional information

This work is supported by the Jiangsu Province Natural Science Foundation of China (BK20151139) and the Fundamental Research Funds for the Central Universities (2012LWA10).

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Wang, H.J., Cao, D.X., Liu, H. et al. Numerical validation for systems of absolute value equations. Calcolo 54, 669–683 (2017). https://doi.org/10.1007/s10092-016-0204-1

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Keywords

  • Systems of absolute value equations
  • Poincaré–Miranda theorem
  • Error bounds

Mathematics Subject Classification

  • 65K05
  • 90C30