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Modulus‐based multigrid methods for linear complementarity problems
Author(s) -
Bai ZhongZhi,
Zhang LiLi
Publication year - 2017
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.2105
Subject(s) - multigrid method , mathematics , convergence (economics) , complementarity (molecular biology) , modulus , linear complementarity problem , fourier analysis , mathematical optimization , fourier transform , algorithm , mathematical analysis , partial differential equation , geometry , nonlinear system , physics , quantum mechanics , biology , economics , genetics , economic growth
Summary By employing modulus‐based matrix splitting iteration methods as smoothers, we establish modulus‐based multigrid methods for solving large sparse linear complementarity problems. The local Fourier analysis is used to quantitatively predict the asymptotic convergence factor of this class of multigrid methods. Numerical results indicate that the modulus‐based multigrid methods of the W‐cycle can achieve optimality in terms of both convergence factor and computing time, and their asymptotic convergence factors can be predicted perfectly by the local Fourier analysis of the corresponding modulus‐based two‐grid methods.