The Convergence Results between Backward USSOR and Jacobi Iterative Matrices
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33093
The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

Keywords: Backward USSOR iterative matrix, Jacobi iterative matrix, convergence, spectral radius

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087868

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1302

References:


[1] R. S. Varga, Matrix Iterative Analysis, 2nd Endition, Springer, Berlin, 2000.
[2] A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
[3] X. P. Liu, Convergence of some iterative methods, Numerical Computing and Computer Applications, 1(1992)58-64 (in Chinese).
[4] N. M. Missirlis, D. J. Evans, The modified preconditioned simultaneous displacement (MPSD) method, Math. Comp. Simulations, XXVI (1984) 257-262.
[5] Z. D. Wang, T. Z. Huang, Comparison results between Jacobi and other iterative methods, J. Comp. Appl. Math. 169(2004)45-51.
[6] Wen Li, Ludwig Elsner, Linzhang Lu, Comparisons os spectral radii and the theorem of Stein-Rosenberg, Linear Algebra Appl.348(2002)283-287.
[7] R. M. Li, Relationship of eigenvalue for USAOR iterative method applied to a class of p-cyclic matrices, Linear Algebra Appl.362(2003)101-108.
[8] A. Hadjidimos, D. Noutsos, M. Tzoumas, Torwards the determination of optimal p-cyclic SSOR, J. Comp. Appl. Math. 90(1996)1-14.
[9] S. Galanis, A. Hadjidimos, D. Noutsos, A Young-Eidson’s type algorithm for complex p-cyclic SOR spectra, Linear Algebra Appl. 286(1999)87-106.
[10] A. Hadjidimos, D. Noutsos, M. Tzoumas, On the exact p-cyclic SSOR convergence domains, Linear Algebra Appl. 232(2003)213-236.
[11] A. Hadjidimos, D. Noutsos, M. Tzoumas, On the convergence domains of the p-cyclic SOR, J. Comp. Appl. Math. 72(1996)63-83.
[12] S. Galanis, A. Hadjidimos, D. Noutsos, Optimal p-cyclic SOR for complex spectra, Linear Algebra Appl. 263(1997)233-260.
[13] D. M. Young, Iterative Solution of Large Linear Systems, NewYork-London, Academic Press, 1971.
[14] A. Hadjidimos, M. Neumann, Superior convergence domains for the p-cyclic SSOR majorizer, J. Comp. Appl. Math. 62(1995)27-40.