A multisplitting method for symmetric linear complementarity problems
The symmetric linear complementarity problem (LCP) is to find an \(n\)-dimensional vector \(z\) such that \(Mz+ q\geq 0\), \(z\geq 0\), \(z^T(Mz+ q)= 0\) for given \(M\) and \(q\). Most of the known methods have their origin in the solution of a system of linear equations and may be classified into pivoting methods and iterative methods. Effective methods are the so-called splitting methods and the multisplitting methods which are parallel iterative methods for solving a system of linear equations. The last methods are able to be implemented on multiprocessors. In the present paper the idea of multisplitting is extended to the symmetric LCP. Convergence theorems are given. Then the multisplitting method is applied to the parallel successive overrelaxation. The effectiveness of multisplitting is examined by some computational experiments.
symmetric linear complementarity problem
scientific article; zbMATH DE number 903474
scientific article