Volume 28, pp. 78-94, 2007-2008.

Minimization of the spectral norm of the SOR operator in a mixed case

A. Hadjidimos and P. Stratis

Abstract

In this work we solve the problem of the minimization of the spectral norm of the SOR operator associated with a block two-cyclic consistently ordered matrix $A\in {\mathbf{C}}^{n,n}$, assuming that the corresponding Jacobi matrix has eigenvalues $\mu \in [-\beta ,\beta ]\cup [-ı\alpha ,ı\alpha ]$, with $\beta \in [0,1)$, $\alpha \in [0,+\mathrm{\infty })$ and $ı=\sqrt{-1}$. Previous results obtained by other researchers are extended.

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Key words

Jacobi and SOR iteration matrices, block two-cyclic consistently ordered matrix, spectral matrix norm

AMS subject classifications

65F10

ETNA articles which cite this article

Vol. 60 (2024), pp. A1-A14 Apostolos Hadjidimos, Xiezhang Li, and Richard S. Varga: Application of the Schur-Cohn Theorem to the precise convergence domain for a p-cyclic SOR iteration matrix