Taiwanese Journal of Mathematics

The Weaker Convergence of Non-stationary Matrix Multisplitting Methods for Almost Linear Systems

Li-Tao Zhang, Ting-Zhu Huang, Shao-Hua Cheng, and Tong-Xiang Gu

Full-text: Open access

Abstract

In 1999, Arnal et al. [Numerical linear algebra and its applications, 6(1999): 79-92] introduced the non-stationary matrix multisplitting algorithms for almost linear systems and studied the convergence of them. In this paper, we generalize Arnal’s algorithms and study the non-stationary matrix multisplitting multi-parameters methods for almost linear systems. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, the convergence results of our new method in this paper are weaker than those of Arnal’s. Finally, numerical examples show that our new convergence results are better and more efficient than Arnal’s.

Article information

Source
Taiwanese J. Math., Volume 15, Number 4 (2011), 1423-1436.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406354

Digital Object Identifier
doi:10.11650/twjm/1500406354

Mathematical Reviews number (MathSciNet)
MR2848964

Zentralblatt MATH identifier
1233.65030

Subjects
Primary: 65F10: Iterative methods for linear systems [See also 65N22] 65F15: Eigenvalues, eigenvectors

Keywords
$H$-matrix $M$-matrix almost linear systems non-stationary matrix multisplitting multi-parameters methods

Citation

Zhang, Li-Tao; Huang, Ting-Zhu; Cheng, Shao-Hua; Gu, Tong-Xiang. The Weaker Convergence of Non-stationary Matrix Multisplitting Methods for Almost Linear Systems. Taiwanese J. Math. 15 (2011), no. 4, 1423--1436. doi:10.11650/twjm/1500406354. https://projecteuclid.org/euclid.twjm/1500406354


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References

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