Inexact multisplitting methods for linear complementarity problems

Authors:
Jun-Liang Dong
Affiliations:
State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We present an inexact multisplitting method for solving the linear complementarity problems, which is based on the inexact splitting method and the multisplitting method. This new method provides a specific realization for the multisplitting method and generalizes many existing matrix splitting methods for linear complementarity problems. Convergence for this new method is proved when the coefficient matrix is an H"+-matrix. Then, two specific iteration forms for this inexact multisplitting method are presented, where the inner iterations are implemented either through a matrix splitting method or through a damped Newton method. Convergence properties for both these specific forms are analyzed, where the system matrix is either an H"+-matrix or a symmetric matrix.