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Post‐processing of Gauss–Seidel iterations
Author(s) -
Křížek Michal,
Liu Liping,
Neittaanmäki Pekka
Publication year - 1999
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199903)6:2<147::aid-nla153>3.0.co;2-u
Subject(s) - gauss–seidel method , mathematics , invertible matrix , iterative method , convergence (economics) , algebraic equation , finite element method , simple (philosophy) , preconditioner , gauss , matrix (chemical analysis) , algebraic number , boundary value problem , mathematical analysis , nonlinear system , algorithm , pure mathematics , philosophy , physics , materials science , epistemology , quantum mechanics , economics , composite material , thermodynamics , economic growth
We examine a simple post‐processing technique when solving the system of n linear algebraic equations Ax = b with a nonsingular matrix using the classical iterative methods such as the Gauss‐Seidel method. We prove that this technique accelerates the convergence of iterations. Its efficiency is demonstrated on a system arising from a finite element approximation of a second order elliptic boundary value problem. Copyright © 1999 John Wiley & Sons, Ltd.