A Preconditioned Gauss-Seidel Iterative Method for Linear Complementarity Problem in Intelligent Materials System

2011 ◽  
Vol 340 ◽  
pp. 3-8 ◽  
Author(s):  
Ban Xiang Duan ◽  
Wen Ying Zeng ◽  
Xiao Ping Zhu

In this paper, the authors first set up new preconditioned Gauss-Seidel iterative method for solving the linear complementarity problem, whose preconditioned matrix is introduced. Then certain elementary operations row are performed on system matrix before applying the Gauss-Seidel iterative method. Moreover the sufficient conditions for guaranteeing the convergence of the new preconditioned Gauss-Seidel iterative method are presented. Lastly we report some computational results with the proposed method.

2021 ◽  
Vol 6 (11) ◽  
pp. 11904-11920
Author(s):  
Xi-Ming Fang ◽  

<abstract><p>In this paper, we consider numerical methods for the linear complementarity problem (LCP). By introducing a positive diagonal parameter matrix, the LCP is transformed into an equivalent fixed-point equation and the equivalence is proved. Based on such equation, the general fixed-point (GFP) method with two cases are proposed and analyzed when the system matrix is a $ P $-matrix. In addition, we provide several concrete sufficient conditions for the proposed method when the system matrix is a symmetric positive definite matrix or an $ H_{+} $-matrix. Meanwhile, we discuss the optimal case for the proposed method. The numerical experiments show that the GFP method is effective and practical.</p></abstract>


2011 ◽  
Vol 204-210 ◽  
pp. 687-690
Author(s):  
Li Pu Zhang ◽  
Ying Hong Xu

Through some modifications on the classical-Newton direction, we obtain a new searching direction for monotone horizontal linear complementarity problem. By taking the step size along this direction as one, we set up a full-step primal-dual interior-point algorithm for monotone horizontal linear complementarity problem. The complexity bound for the algorithm is derived, which is the best-known for linear complementarity problem.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 503
Author(s):  
Shiliang Wu ◽  
Cuixia Li ◽  
Praveen Agarwal

In this paper, we obtain a new equivalent fixed-point form of the linear complementarity problem by introducing a relaxed matrix and establish a class of relaxed modulus-based matrix splitting iteration methods for solving the linear complementarity problem. Some sufficient conditions for guaranteeing the convergence of relaxed modulus-based matrix splitting iteration methods are presented. Numerical examples are offered to show the efficacy of the proposed methods.


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