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An improved error bound for linear complementarity problems for B-matrices.

Lei Gao1, Chaoqian Li2

  • 1School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shannxi 721013 P.R. China.

Journal of Inequalities and Applications
|July 7, 2017
PubMed
Summary
This summary is machine-generated.

A novel error bound for B-matrix linear complementarity problems offers improved accuracy. This new bound is demonstrated to be sharper than existing methods, enhancing computational efficiency.

Keywords:
B-matrixerror boundlinear complementarity problem

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Area of Science:

  • Numerical analysis
  • Matrix theory
  • Optimization

Background:

  • The linear complementarity problem (LCP) is a fundamental problem in mathematical programming.
  • Error bounds are crucial for analyzing the convergence and efficiency of algorithms solving LCPs.
  • Existing error bounds for B-matrix LCPs have limitations in terms of sharpness.

Purpose of the Study:

  • To present a new, improved error bound for the linear complementarity problem (LCP) when the involved matrix is a B-matrix.
  • To demonstrate that the new error bound surpasses the result presented by Li et al. (2016).
  • To establish sufficient conditions under which the new bound is sharper than that of García-Esnaola and Peña (2009).

Main Methods:

  • Derivation of a new error bound using matrix properties.
  • Comparative analysis of the new bound against existing bounds in the literature.
  • Identification of specific conditions for bound superiority.

Main Results:

  • A novel error bound for B-matrix LCPs has been established.
  • The new bound demonstrably improves upon the result from Li et al. (2016).
  • Sufficient conditions are identified for the new bound to be sharper than the bound by García-Esnaola and Peña (2009).

Conclusions:

  • The proposed error bound offers a significant advancement for B-matrix LCPs.
  • The findings contribute to the development of more efficient algorithms for solving LCPs.
  • This work refines the theoretical understanding of error bounds in LCP analysis.