The Fast Iterative Algorithms For A Class Of Linear Complementartiy Problems Arising From Elastic Contact Problems

The elastic normal contact problems can be transformed into linear complementarity problems involving the system matrices of Toeplitz structure.The more precise solutions are needed,the smaller the mesh size have,and the scale of the system matrices of the linear complementarity problems will be larger.The modulus-based matrix splitting iteration method is one of the most efficient method for solving the large-scale problems,and the preprocessing technology can improve the computational speed of the algorithms.In this paper,the modulus-based matrix splitting iteration methods are combined with precondition technique or matrix splitting methods,several kinds of fast algorithms for solving linear complementarity problems with Toeplitz structure are introduced as follows:Firstly,we introduced a class of preconditioned modulus-based matrix splitting iteration method that combines two kinds of existing circulant preconditioners with the improved modulus-based matrix splitting iteration method.The convergence and the relevant numerical experimental results are both presented.Secondly,a class of preconditioned modulus-based matrix multi-splitting block iteration method is presented to solve the large-scale problems by combining preprocessing method with matrix multi-splitting method,which can make the problem divided into several small scales problems.The convergence and the numerical results are both given.Thirdly,a class of block preconditioned modulus-based matrix splitting iteration method is constructed for solving the linear complementarity problems with positive definite level-2 symmetric BTTB matrices.The convergence and the numerical results are both given.At last,according to C-S splitting of the Toeplitz matrix,a class of modulus-based matrix CSCS iteration method has been presented.The convergence and the numerical results are both given.