预条件IMGS迭代方法的比较定理

Abstract

Abstract:

In this paper, by comparing with the spectral radiuses of the iterative methods, the authors prove, for the first time, that the IMGS method^[1-2] with the preconditioner I+S_α is faster than the basic AOR iterative method, and then prove that the preconditioned SOR method is
faster than the basic SOR method. Finally, the authors prove the monotony of the spectral radius with respect to the parameter and
improve some recent known results.

Key words: Preconditioner, Gauss-Seidel iteration, AOR iteration, M-matrix, Linear system

CLC Number:

65F10

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LI Wei-Cheng, JIANG Yao-Lin. Comparison Theroems for the IMGS Iterative Method with Preconditioner[J].Acta mathematica scientia,Series A, 2011, 31(4): 880-886.

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Comparison Theroems for the IMGS Iterative Method with Preconditioner

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