Comparison Results between Jacobi and USSOR Iterative Methods

Ting Zhou; Shi Guang Zhang

doi:10.4028/www.scientific.net/AMR.989-994.1790

Paper Titles

A Fuzzy Clustering Algorithm of Web Customers Based on Attributes Reduction
p.1775

The Application of Graph Model in the Cultural Archives
p.1779

Deobfuscate Non-Returning Calls and Call-Stack Tampering in Instruction Traces
p.1782

Constructing Attractors via the Improved Eugenics Genetic Algorithm
p.1786

Comparison Results between Jacobi and USSOR Iterative Methods
p.1790

Convergence Results of the Improving Modified Gauss-Seidel (IMGS) Iterative Method for a Symmetric Positive Definite Matrix
p.1794

A Fast Algorithm for Computing the Determinants of the Heptadiagonal Matrices
p.1798

Two-Parameter Conjugate Gradient Projection Method and its Application
p.1802

Generalized J Sets Based on Periodic Orbit and Attract Time
p.1806

HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 989-994Comparison Results between Jacobi and USSOR...

Comparison Results between Jacobi and USSOR Iterative Methods

Abstract:

In this paper, some comparison results between Jacobi and USSOR iteration for solving nonsingular linear systems are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of USSOR iterative matrix under some conditions. A numerical example is also given to illustrate our results.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Advanced Materials Research (Volumes 989-994)

Pages:

1790-1793

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.989-994.1790

Citation:

Cite this paper

Online since:

July 2014

Authors:

Ting Zhou*, Shi Guang Zhang

Keywords:

Comparison Results, Jacobi Iteration, Spectral Radius, USSOR Iteration

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] R. S. Varga: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, NJ (1981).

Google Scholar

[2] A. Berman, R. J. Plemmons: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York, 1979, reprinted by SIAM, Philadelphia, PA (1994).

Google Scholar

[3] W. F. Wang, D. W. Chang: The New Preconditioned USSOR Iterative Method and Comparison of Convergence . Journal of Inner Mongolia Normal University (Natural Science Edition), Vol 32. No. 2(2008), pp.158-161.

Google Scholar

[4] Z. D. Wang, T. Z. Huang: Comparison results between Jacobi and other iterative methods. Journal of Computational and Applied Mathematics, Vol. 169(2004), pp.45-51.

DOI: 10.1016/j.cam.2003.10.017

Google Scholar

[5] H. X. Chen: Convergent and divergent relationship between MPSD iterative method and Jacobi method. Comm. Appl. Math. Comput. Vol. 14. No. 1 (2000), pp.1-8.

Google Scholar

[6] J. H. Yun: A note on the improving modified Gauss-Seidel (IMGS)method. Applied Mathematics and Computation Vol. 184(2007), pp.674-679.

DOI: 10.1016/j.amc.2006.06.067

Google Scholar

[7] X. Z. Wang, T. Z. Huang, Y. D. Fu: Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems, J. Comput. Appl. Math., vol. 206(2007), pp.726-732.

DOI: 10.1016/j.cam.2006.08.034

Google Scholar