Convergence and the optimal choice of the relaxation parameter for a class of iterative methods

M. A. El-Gebeily; M. B.M. Elgindi

doi:10.1016/j.amc.2005.04.086

Convergence and the optimal choice of the relaxation parameter for a class of iterative methods

M. A. El-Gebeily
, M. B.M. Elgindi^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A necessary condition for the convergence of the iterative scheme u _i+1 = (I - γT)u_i + F is given. The existence of a value γ that minimizes the spectral radius of the iteration matrix (I - γT) is proved. The explicit expression of the optimizing γ in terms of the eigenvalues of T is also given.

Original language	English
Pages (from-to)	353-364
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	174
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2005.04.086
State	Published - 1 Mar 2006

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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title = "Convergence and the optimal choice of the relaxation parameter for a class of iterative methods",

abstract = "A necessary condition for the convergence of the iterative scheme u i+1 = (I - γT)ui + F is given. The existence of a value γ that minimizes the spectral radius of the iteration matrix (I - γT) is proved. The explicit expression of the optimizing γ in terms of the eigenvalues of T is also given.",

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N2 - A necessary condition for the convergence of the iterative scheme u i+1 = (I - γT)ui + F is given. The existence of a value γ that minimizes the spectral radius of the iteration matrix (I - γT) is proved. The explicit expression of the optimizing γ in terms of the eigenvalues of T is also given.

AB - A necessary condition for the convergence of the iterative scheme u i+1 = (I - γT)ui + F is given. The existence of a value γ that minimizes the spectral radius of the iteration matrix (I - γT) is proved. The explicit expression of the optimizing γ in terms of the eigenvalues of T is also given.

UR - https://www.scopus.com/pages/publications/33344474728

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DO - 10.1016/j.amc.2005.04.086

M3 - Article

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EP - 364

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Convergence and the optimal choice of the relaxation parameter for a class of iterative methods

Abstract

ASJC Scopus subject areas

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