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Volume 8, Issue 2
Upper Bounds of the Spectral Radii of Some Iterative Matrices

Jia-Gan Hu

J. Comp. Math., 8 (1990), pp. 118-127.

Published online: 1990-08

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  • Abstract

In this paper, the concept of optimally scaled matrix and the estimate of $\|M^{-1}N\|_{\infty}$ in our previous paper are used to find the upper bounds of the spectral radii of the iterative matrices SOR, SSOR, AOR and SAOR. The sharpness of the upper bounds of the spectral radii of SOR and AOR is established. The proofs are very intuitive and may be considered as the geometrical interpretations of our theorems.

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@Article{JCM-8-118, author = {Hu , Jia-Gan}, title = {Upper Bounds of the Spectral Radii of Some Iterative Matrices}, journal = {Journal of Computational Mathematics}, year = {1990}, volume = {8}, number = {2}, pages = {118--127}, abstract = {

In this paper, the concept of optimally scaled matrix and the estimate of $\|M^{-1}N\|_{\infty}$ in our previous paper are used to find the upper bounds of the spectral radii of the iterative matrices SOR, SSOR, AOR and SAOR. The sharpness of the upper bounds of the spectral radii of SOR and AOR is established. The proofs are very intuitive and may be considered as the geometrical interpretations of our theorems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9425.html} }
TY - JOUR T1 - Upper Bounds of the Spectral Radii of Some Iterative Matrices AU - Hu , Jia-Gan JO - Journal of Computational Mathematics VL - 2 SP - 118 EP - 127 PY - 1990 DA - 1990/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9425.html KW - AB -

In this paper, the concept of optimally scaled matrix and the estimate of $\|M^{-1}N\|_{\infty}$ in our previous paper are used to find the upper bounds of the spectral radii of the iterative matrices SOR, SSOR, AOR and SAOR. The sharpness of the upper bounds of the spectral radii of SOR and AOR is established. The proofs are very intuitive and may be considered as the geometrical interpretations of our theorems.

Jia-Gan Hu. (1970). Upper Bounds of the Spectral Radii of Some Iterative Matrices. Journal of Computational Mathematics. 8 (2). 118-127. doi:
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