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On the preconditioned GAOR method for a linear complementarity problem with an M-matrix.

Shu-Xin Miao1, Dan Zhang1

  • 1College of Mathematics and Statistics, Northwest Normal University, Lanzhou, People's Republic of China.

Journal of Inequalities and Applications
|August 24, 2018
PubMed
Summary
This summary is machine-generated.

A new preconditioned generalized accelerated over-relaxation (GAOR) method is introduced for solving linear complementarity problems with M-matrices. This novel approach demonstrates accelerated convergence compared to existing methods, as confirmed by numerical examples.

Keywords:
Linear complementarity problemM-matrixPreconditioned GAOR methodPreconditioner

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Area of Science:

  • Numerical analysis
  • Optimization theory

Background:

  • Linear complementarity problems (LCPs) are fundamental in applied mathematics and game theory.
  • Existing methods like the preconditioned GAOR method offer solutions but have limitations in convergence speed.

Purpose of the Study:

  • To propose a novel preconditioned generalized accelerated over-relaxation (GAOR) method for solving linear complementarity problems (LCPs) specifically for M-matrices.
  • To analyze the convergence properties of the new method.
  • To demonstrate its superiority over existing methods.

Main Methods:

  • Development of a new preconditioned GAOR iterative method.
  • Theoretical analysis of the convergence of the proposed method.
  • Comparative numerical experiments against existing GAOR methods.

Main Results:

  • The proposed preconditioned GAOR method exhibits faster convergence rates for LCPs with M-matrices.
  • The new method accelerates the convergence compared to the original GAOR and the previously proposed preconditioned GAOR method.
  • Numerical results validate the theoretical convergence analysis.

Conclusions:

  • The new preconditioned GAOR method is an effective and efficient technique for solving linear complementarity problems involving M-matrices.
  • This advancement offers improved computational performance in solving specific classes of LCPs.