Note on error bounds for linear complementarity problems of Nekrasov matrices
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García-Esnaola and Peña (Numer. Algor. 67, 655–667, 2014) presented an error bound involving a parameter for linear complementarity problems of Nekrasov matrices. This bound is not effective in some cases because it tends to infinity when the involved parameter tends to zero. In this paper, the optimal value of this error bound is determined completely by using the monotonicity of functions of this parameter. Numerical examples are given to verify the corresponding results.
KeywordsLinear complementarity problems Error bounds Nekrasov matrices P-matrices
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The authors would like to thank the associate editor Prof. Xiaojun Chen and anonymous referees for their valuable suggestions, and also thank Mengting Gan for her discussion on 32 cases.
The first author is supported partly by the Applied Basic Research Programs of Science and Technology Department of Yunnan Province [grant number 2018FB001], Outstanding Youth Cultivation Project for Yunnan Province [grant number 2018YDJQ021], Program for Excellent Young Talents in Yunnan University, and CAS ’Light of West China’ Program. His work was finished, while he was a visiting scholar at Shanghai Key Laboratory of Contemporary Applied Mathematics of Fudan University during 2017 and 2018.
The third author is supported partly by National Natural Science Foundations of China [grant number 11461080].
The fourth author is supported partly by National Natural Science Foundations of China [grant number 11861077].
The fifth author is supported partly by National Natural Science Foundations of China [grant number 11771099] and Shanghai Municipal Education Commission.