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

M. A. El-Gebeily, Mohamed Elgindi

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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

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ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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