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Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems
Author(s) -
Bai ZhongZhi,
Zhang LiLi
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1835
Subject(s) - mathematics , gauss–seidel method , jacobi method , linear system , iterative method , convergence (economics) , relaxation (psychology) , linear complementarity problem , matrix (chemical analysis) , system of linear equations , algorithm , mathematical analysis , nonlinear system , psychology , social psychology , physics , materials science , quantum mechanics , economics , composite material , economic growth
SUMMARY By an equivalent reformulation of the linear complementarity problem into a system of fixed‐point equations, we construct modulus‐based synchronous multisplitting iteration methods based on multiple splittings of the system matrix. These iteration methods are suitable to high‐speed parallel multiprocessor systems and include the multisplitting relaxation methods such as Jacobi, Gauss–Seidel, successive overrelaxation, and accelerated overrelaxation of the modulus type as special cases. We establish the convergence theory of these modulus‐based synchronous multisplitting iteration methods and their relaxed variants when the system matrix is an H + ‐matrix. Numerical results show that these new iteration methods can achieve high parallel computational efficiency in actual implementations. Copyright © 2012 John Wiley & Sons, Ltd.