×

On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices. (English) Zbl 1101.65033

The convergence of a generalized accelerated overrelaxation (AOR) method to solve the linear system \(Hy= f\), namely: \(y^{k+1}= \ell_{\omega,r}y^{(k)}+\omega k\), is investigated. Sufficient convergence conditions for \(\omega\) and \(r\) are obtained, for \(H\) being a weak diagonally dominant matrix.

MSC:

65F10 Iterative numerical methods for linear systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Froberg, C., Numerical Mathematics, Theory and computer applications (1985), The Benjamin Cummings Publishing Company, Inc.
[2] Hadjidimos, A., Accelerated overrelaxation method, Math. Comput., 32, 141, 149-157 (1978) · Zbl 0382.65015
[3] A. Hadjidimos, A. Yeyios, The Principle of extrapolation in connection with the accelerated overrelaxation (AOR) method, T. R. No. 8, Department of Mathematics, University of Ioannina, Ioannina, Greece, 1978.; A. Hadjidimos, A. Yeyios, The Principle of extrapolation in connection with the accelerated overrelaxation (AOR) method, T. R. No. 8, Department of Mathematics, University of Ioannina, Ioannina, Greece, 1978. · Zbl 0428.65015
[4] Martins, M. M., On an accelerated overrelaxation iterative method for linear systems with diagonally dominant matrix, Math. Comput., 35, 152, 1269-1273 (1980) · Zbl 0463.65021
[5] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall · Zbl 0133.08602
[6] Young, D. M., Iterative Solution for Large Linear Systems (1971), Academic Press: Academic Press New York · Zbl 0204.48102
[7] Yuan, J. Y., Numerical methods for generalized least squares problems, J. Comput. Appl. Math., 66, 571-584 (1996) · Zbl 0858.65043
[8] Yuan, J. Y.; Jin, X. Q., Convergence of the generalized AOR method, Appl. Math. Comput., 99, 35-46 (1999) · Zbl 0961.65029
[9] Searle, S.; Casella, G.; McCulloch, C., Variance Components (1992), Willy/Interscience: Willy/Interscience New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.