New estimations of the spectral radii of J, G-S and SOR iterative matrices for a class of linear systems. (English) Zbl 1117.65048
Estimates of the spectral radius of iterative matrices in terms of row sums are often used. Roughly speaking, here uniform row sums are replaced by individual ones. This leads to improvements in the numerical examples that are presented.
Reviewer: Dietrich Braess (Bochum)
MSC:
65F10 | Iterative numerical methods for linear systems |
15A42 | Inequalities involving eigenvalues and eigenvectors |
Keywords:
SOR iteration; spectral radius; diagonal dominance; Jacobi method; Gauss-Seidel method; successive overrelaxation; numerical examplesReferences:
[1] | James K. R., Mathematics of Computation 10 pp 478– (1973) |
[2] | James K. R., Mathematics of Computation 12 pp 137– (1975) |
[3] | DOI: 10.1090/S0025-5718-1980-0583503-4 · doi:10.1090/S0025-5718-1980-0583503-4 |
[4] | DOI: 10.1090/S0025-5718-1981-0616363-4 · doi:10.1090/S0025-5718-1981-0616363-4 |
[5] | DOI: 10.1016/j.cam.2004.07.029 · Zbl 1063.65028 · doi:10.1016/j.cam.2004.07.029 |
[6] | DOI: 10.1080/00207169408804271 · Zbl 0828.65028 · doi:10.1080/00207169408804271 |
[7] | DOI: 10.1016/S0377-0427(96)00061-1 · Zbl 0872.65027 · doi:10.1016/S0377-0427(96)00061-1 |
[8] | Herceg D., Zeitschrift für Angewandte Mathematik und Mechanik 71 pp 815– (1991) |
[9] | Cvetkovic L. J., Journal of Computational Mathematics 8 pp 128– (1990) |
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.