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

Ping Fan Dai; Ji Cheng Li; Yao Tang Li; Jianchao Bai

doi:10.1016/j.cam.2016.11.034

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

Ping Fan Dai
, Ji Cheng Li
, Yao Tang Li
, Jianchao Bai

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	100-112
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	317
DOIs	https://doi.org/10.1016/j.cam.2016.11.034
State	Published - 1 Jun 2017

Keywords

Comparison theorem
Linear complementarity problems
Preconditioner
SSOR method

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10.1016/j.cam.2016.11.034

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title = "A general preconditioner for linear complementarity problem with an M-matrix",

abstract = "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.",

keywords = "Comparison theorem, Linear complementarity problems, Preconditioner, SSOR method",

author = "Dai, \{Ping Fan\} and Li, \{Ji Cheng\} and Li, \{Yao Tang\} and Jianchao Bai",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

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doi = "10.1016/j.cam.2016.11.034",

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TY - JOUR

T1 - A general preconditioner for linear complementarity problem with an M-matrix

AU - Dai, Ping Fan

AU - Li, Ji Cheng

AU - Li, Yao Tang

AU - Bai, Jianchao

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

KW - Comparison theorem

KW - Linear complementarity problems

KW - Preconditioner

KW - SSOR method

UR - https://www.scopus.com/pages/publications/85006381819

U2 - 10.1016/j.cam.2016.11.034

DO - 10.1016/j.cam.2016.11.034

M3 - 文章

AN - SCOPUS:85006381819

SN - 0377-0427

VL - 317

SP - 100

EP - 112

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

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

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Keywords

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