MSSOR-based alternating direction method for symmetric positive-definite linear complementarity problems

2014 ◽  
Vol 68 (3) ◽  
pp. 631-644 ◽  
Author(s):  
Jian-Jun Zhang
Keyword(s):  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Alternating Direction Method ◽  
Symmetric Positive Definite ◽  
Alternating Direction

Almost Definite Matrices Revisited

2015 ◽  
Vol 29 ◽  
pp. 102-119
Author(s):  
K. Sivakumar ◽  
Ar. Meenakshi ◽  
Projesh Choudhury
Keyword(s):  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Positive Semidefinite ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Real Matrix ◽  
Positive Semidefinite Matrices ◽  
Matrix Classes ◽  
Basic Properties

A real matrix A is called as an almost definite matrix if ⟨x, Ax⟩ = 0 ⇒ Ax = 0. This notion is revisited. Many basic properties of such matrices are established. Several characterizations for a matrix to be an almost definite matrix are presented. Comparisons of certain properties of almost definite matrices with similar properties for positive definite or positive semidefinite matrices are brought to the fore. Interconnections with matrix classes arising in the theory of linear complementarity problems are discussed briefly.

scholarly journals A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yuan Li ◽  
Hai-Shan Han ◽  
Dan-Dan Yang
Keyword(s):  
Newton Method ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Singular Values ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Generalized Newton Method ◽  
Absolute Value ◽  
The Matrix ◽  
Generalized Newton

We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient.

Relaxed Parallel Modulus-Based Matrix Multisplitting Iterative Methods for Linear Complementarity Problem

2013 ◽  
Vol 741 ◽  
pp. 117-122 ◽  
Author(s):  
Ban Xiang Duan ◽  
Dong Hai Zeng ◽  
Ai Min Yu
Keyword(s):  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Coefficient Matrix ◽  
Positive Definite Matrices ◽  
Convergence Conditions ◽  
Matrix Multisplitting ◽  
Symmetric Positive Definite ◽  
Iteration Methods ◽  
Symmetric Positive Definite Matrices

In this paper, the authors establish a class of relaxed parallel modulus-based matrix multisplitting iteration methods for large sparse linear complementarity problems, based on the multisplittings of the coefficient matrix. And then, they prove their convergence when the system matrices are H-matrix with positive diagonal elements. These results naturally present convergence conditions for the symmetric positive definite matrices and the M-matrices.

Sign in / Sign up

Export Citation Format

Share Document