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

M. A. El-Gebeily, Mohamed Elgindi

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)353-364
Number of pages12
JournalApplied Mathematics and Computation
Volume174
Issue number1
DOIs
Publication statusPublished - 1 Mar 2006
Externally publishedYes

Fingerprint

Spectral Radius
Iterative Scheme
Iterative methods
Eigenvalue
Minimise
Iteration
Necessary Conditions
Class

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Convergence and the optimal choice of the relaxation parameter for a class of iterative methods. / El-Gebeily, M. A.; Elgindi, Mohamed.

In: Applied Mathematics and Computation, Vol. 174, No. 1, 01.03.2006, p. 353-364.

Research output: Contribution to journalArticle

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