A general preconditioner for linear complementarity problem with an M-matrix

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:317

Article

Dai, Ping-Fan^1,2  Li, Ji-Cheng¹  Li, Yao-Tang³  Bai, Jianchao¹ 

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[2] Sanming Univ, Dept Informat Engn, Sanming 365004, Fujian, Peoples R China

[3] Yunnan Univ, Sch Math & Stat, Kunming 650091, Yunnan, Peoples R China

关键词: Linear complementarity problems;    Preconditioner;    SSOR method;    Comparison theorem;   

DOI  :  10.1016/j.cam.2016.11.034

来源: Elsevier

【 摘 要 】

In this paper, we first present a general preconditioner P for solving linear complementarity problem (LCP) associated with an M-matrix A and a vector f, and prove that the LCP(A, f) is equivalent to the LCP(PA, Pf). Then based on this general preconditioner P, two preconditioned SSOR methods for solving the linear complementarity problems are proposed. We show that this general preconditioner P accelerates the convergence of two SSOR methods under the assumption that PA is a Z -matrix. In addition, we also give a practically concrete choice for the preconditioner P satisfying aforementioned assumption. Numerical examples are used to illustrate the theoretical results obtained. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free