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Modulus‐based matrix splitting iteration methods for linear complementarity problems
Author(s) -
Bai ZhongZhi
Publication year - 2010
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.680
Subject(s) - mathematics , positive definite matrix , linear complementarity problem , modulus , matrix splitting , matrix (chemical analysis) , convergence (economics) , relaxation (psychology) , complementarity (molecular biology) , iterative method , mathematical analysis , symmetric matrix , algorithm , state transition matrix , nonlinear system , geometry , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , biology , composite material , genetics , psychology , social psychology , economics , economic growth
For the large sparse linear complementarity problems, by reformulating them as implicit fixed‐point equations based on splittings of the system matrices, we establish a class of modulus‐based matrix splitting iteration methods and prove their convergence when the system matrices are positive‐definite matrices and H + ‐matrices. These results naturally present convergence conditions for the symmetric positive‐definite matrices and the M ‐matrices. Numerical results show that the modulus‐based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency. Copyright © 2009 John Wiley & Sons, Ltd.