TY - JOUR

T1 - On the convergence of a matrix splitting algorithm for the symmetric monotone linear complementarity problem

AU - Luo, Zhi Quan

AU - Tseng, Paul

PY - 1991/1/1

Y1 - 1991/1/1

N2 - A matrix splitting algorithm for the linear complementarity problem is considered, where the matrix is symmetric positive semidefinite. It is shown that if the splitting is regular, then the iterates generated by the algorithm are well defined and converge to a solution. This result resolves in the affirmative a long standing question about the convergence of the point successive overrelaxation (SOR) method for solving this problem. This result is also extended to related iterative methods. As direct consequences, convergence of the methods of, respectively, Aganagic, Cottle et al., Mangasarian, Pang, and others, is obtained, without making any additional assumptions on the problem.

AB - A matrix splitting algorithm for the linear complementarity problem is considered, where the matrix is symmetric positive semidefinite. It is shown that if the splitting is regular, then the iterates generated by the algorithm are well defined and converge to a solution. This result resolves in the affirmative a long standing question about the convergence of the point successive overrelaxation (SOR) method for solving this problem. This result is also extended to related iterative methods. As direct consequences, convergence of the methods of, respectively, Aganagic, Cottle et al., Mangasarian, Pang, and others, is obtained, without making any additional assumptions on the problem.

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U2 - 10.1137/0329057

DO - 10.1137/0329057

M3 - Article

AN - SCOPUS:0026223084

VL - 29

SP - 1037

EP - 1060

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 5

ER -