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The modulus‐based matrix splitting algorithms for a class of weakly nonlinear complementarity problems
Author(s) -
Huang Na,
Ma Changfeng
Publication year - 2016
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.2039
Subject(s) - mathematics , discretization , nonlinear complementarity problem , matrix splitting , linear complementarity problem , complementarity theory , matrix (chemical analysis) , complementarity (molecular biology) , positive definite matrix , modulus , mixed complementarity problem , nonlinear system , algorithm , class (philosophy) , convergence (economics) , convergent matrix , mathematical analysis , symmetric matrix , state transition matrix , computer science , geometry , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , artificial intelligence , biology , economics , composite material , genetics , economic growth
Summary In this paper, we study a class of weakly nonlinear complementarity problems arising from the discretization of free boundary problems. By reformulating the complementarity problems as implicit fixed‐point equations based on splitting of the system matrices, we propose a class of modulus‐based matrix splitting algorithms. We show their convergence by assuming that the system matrix is positive definite. Moreover, we give several kinds of typical practical choices of the modulus‐based matrix splitting iteration methods based on the different splitting of the system matrix. Numerical experiments on two model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of our modulus‐based matrix splitting algorithms. Copyright © 2016 John Wiley & Sons, Ltd.