Modulus‐based synchronous two‐stage multisplitting iteration methods for linear complementarity problems

Modulus‐based synchronous two‐stage multisplitting iteration methods for linear complementarity problems

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Article ID: iaor2013596
Volume: 62
Issue: 1
Start Page Number: 59
End Page Number: 77
Publication Date: Jan 2013
Journal: Numerical Algorithms
Authors: ,
Keywords: linear complementarity, parallel algorithms
Abstract:

In order to solve large sparse linear complementarity problems on parallel multiprocessor systems, we construct modulus‐based synchronous two‐stage multisplitting iteration methods based on two‐stage multisplittings of the system matrices. These iteration methods include the multisplitting relaxation methods such as Jacobi, Gauss–Seidel, SOR and AOR of the modulus type as special cases. We establish the convergence theory of these modulus‐based synchronous two‐stage multisplitting iteration methods and their relaxed variants when the system matrix is an H + ‐matrix. Numerical results show that in terms of computing time the modulus‐based synchronous two‐stage multisplitting relaxation methods are more efficient than the modulus‐based synchronous multisplitting relaxation methods in actual implementations.

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