Convergence Analysis of the Projected SOR Iteration Method for Horizontal Linear Complementarity Problems

doi:10.1007/s42967-023-00354-x

Abstract

Abstract: Recently, the projected Jacobi (PJ) and projected Gauss-Seidel (PGS) iteration methods have been studied for solving the horizontal linear complementarity problems (HLCPs). To further improve the convergence rates of the PJ and PGS iteration methods, by using the successive overrelaxation (SOR) matrix splitting technique, a projected SOR iteration method is introduced in this paper to solve the HLCP. Convergence analyses are carefully studied when the system matrices are strictly diagonally dominant and irreducibly diagonally dominant. The newly obtained convergence results greatly extend the current convergence theory. Finally, two numerical examples are given to show the effectiveness of the proposed PSOR iteration method and its advantages over the recently proposed PJ and PGS iteration methods.

Key words: Horizontal linear complementarity problem (HLCP), Matrix splitting, Projected method, Successive overrelaxation (SOR) iteration, Convergence

Qin-Qin Shen, Geng-Chen Yang, Chen-Can Zhou. Convergence Analysis of the Projected SOR Iteration Method for Horizontal Linear Complementarity Problems[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1617-1638.

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