H-矩阵非线性互补问题基于模的矩阵分裂迭代法改进的收敛性定理

Abstract

Abstract:

In this paper, we proved the convergence theories of the modulus-based matrix splitting iteration methods and the corresponding acceleration method for nonlinear complementarity problems of $H$-matrices in a weaker condition. It implies that we have more choices for the splitting $A=M-N$ which makes the modulus-based matrix splitting iteration methods converge. The improved convergence theories extend the scope of modulus-based matrix splitting iteration methods in applications.

Key words: Nonlinear complementarity problem, Modulus-based matrix splitting iteration method, $H$-matrix, Convergence theorem

CLC Number:

O241

Changfeng Ma,Feiyang Ma. The Improved Convergence Theorems of Modulus-Based Matrix Splitting Iteration Methods for a Class of Nonlinear Complementarity Problems with H-Matrices[J].Acta mathematica scientia,Series A, 2022, 42(2): 583-593.

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References 33

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非线性函数	Iter	CPU	Res
$\phi_1(z)$	26	0.0010	8.5203e-006
$\phi_2(z)$	26	0.0010	8.0783e-006
$\phi_3(z)$	27	0.0010	7.0378e-006
$\phi_4(z)$	24	0.0001	8.9217e-006
$\phi_5(z)$	27	0.0370	6.7821e-006

$n$	情形1:			情形2:
	Iter	CPU	Res	Iter	CPU	Res
$20$	26	0.0010	8.5203e-006	26	0.0010	8.5203e-006
$40$	26	0.0010	8.0783e-006	26	0.0010	8.5203e-006
$60$	27	0.0010	7.0378e-006	26	0.0010	8.5203e-006
$80$	24	0.0001	8.9217e-006	26	0.0010	8.5203e-006
$200$	27	0.0370	6.7821e-006	26	0.0010	8.5203e-006

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The Improved Convergence Theorems of Modulus-Based Matrix Splitting Iteration Methods for a Class of Nonlinear Complementarity Problems with H-Matrices

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