Quasi-Chebyshev accelerated iteration methods based on optimization for linear systems
| Autor: | Chuan-Long Wang, Guo-Yan Meng, Rui-Ping Wen |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Physics::Computational Physics
Chebyshev polynomials Preconditioner Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Chebyshev iteration Mathematics::Numerical Analysis Computational Mathematics Computational Theory and Mathematics Fixed-point iteration Modeling and Simulation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Chebyshev pseudospectral method Modified Richardson iteration Chebyshev equation Chebyshev nodes Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 66:934-942 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2013.06.016 |
| Popis: | In this paper, we present a quasi-Chebyshev accelerated iteration method for solving a system of linear equations. Compared with the Chebyshev semi-iterative method, the main difference is that the parameter ω is not obtained by a Chebyshev polynomial but by optimization models. We prove that the quasi-Chebyshev accelerated iteration method is unconditionally convergent if the original iteration method is convergent, and also discuss the convergence rate. Finally, three numerical examples indicate that our method is more efficient than the Chebyshev semi-iterative method. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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