A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems

In this paper, a relaxation modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix splitting iteration methods. The convergence analysis and the strategy of the choice of the parameters are given. Numerical examples show that the proposed methods are efficient and accelerate the convergence performance with less iteration steps and CPU times.

[1]  A. Frommer,et al.  Convergence of relaxed parallel multisplitting methods , 1989 .

[2]  Wen Li,et al.  A general modulus-based matrix splitting method for linear complementarity problems of HH-matrices , 2013, Appl. Math. Lett..

[3]  Apostolos Hadjidimos,et al.  A New Iterative Criterion for H-Matrices , 2006, SIAM J. Matrix Anal. Appl..

[4]  Katta G. Murty,et al.  Linear complementarity, linear and nonlinear programming , 1988 .

[5]  Zhong-Zhi Bai,et al.  Modulus‐based matrix splitting iteration methods for linear complementarity problems , 2010, Numer. Linear Algebra Appl..

[6]  A. Hadjidimos,et al.  Is A∈Cn,n a general H-matrix? , 2012 .

[7]  Apostolos Hadjidimos,et al.  Nonstationary Extrapolated Modulus Algorithms for the solution of the Linear Complementarity Problem , 2009 .

[8]  Van Bokhoven.  Piecewise-linear modelling and analysis , 1981 .

[9]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[10]  Li-Li Zhang,et al.  Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems , 2013, Appl. Math. Lett..

[11]  Zhong-Zhi Bai,et al.  On the Convergence of the Multisplitting Methods for the Linear Complementarity Problem , 1999, SIAM J. Matrix Anal. Appl..

[12]  Li-Li Zhang,et al.  Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems , 2013, Numer. Linear Algebra Appl..

[13]  Hua Zheng,et al.  A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems , 2016 .

[14]  Ning Zheng,et al.  Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem , 2012, Numerical Algorithms.

[15]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[16]  Li-Li Zhang,et al.  Two-step modulus-based matrix splitting iteration method for linear complementarity problems , 2011, Numerical Algorithms.

[17]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[18]  Li-Li Zhang,et al.  Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems , 2012, Numerical Algorithms.

[19]  Mei-Qun Jiang,et al.  A modified modulus method for symmetric positive‐definite linear complementarity problems , 2009, Numer. Linear Algebra Appl..

[20]  Apostolos Hadjidimos,et al.  On Iterative Solution for Linear Complementarity Problem with an H+-Matrix , 2012, SIAM J. Matrix Anal. Appl..