Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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PRECONDITIONED SSOR METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEM WITH M-MATRIX

  • Zhang, Dan (College of Mathematics and Statistics Northwest Normal University)
  • Received : 2017.10.19
  • Accepted : 2019.01.22
  • Published : 2019.04.30
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Abstract

In this paper, we consider the preconditioned iterative methods for solving linear complementarity problem associated with an M-matrix. Based on the generalized Gunawardena's preconditioner, two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method. Numerical examples are used to illustrate the theoretical results.

Keywords

TABLE 1. ρ(B-1 C) and ρ($\tilde{B}^{-1}\tilde{C}$) with α = 2/3 and ω = 1.1 for Example 5.1

DBSHCJ_2019_v34n2_657_t0001.png 이미지

TABLE 2. ρ(B-1C) and ρ($\tilde{B}^{-1}\tilde{C}$) with α = 2/3 and ω = 0.5 for Example 5.1

DBSHCJ_2019_v34n2_657_t0002.png 이미지

TABLE 3. IT, CPU and ρ with different n and ω for Example 5.2

DBSHCJ_2019_v34n2_657_t0003.png 이미지

TABLE 4

DBSHCJ_2019_v34n2_657_t0004.png 이미지

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