Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the Convergence Rate of Additive Iterative Methods

On the Convergence Rate of Additive Iterative Methods Di erential Equations, Vol. 37, No. 7, 2001, pp. 909{922. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 7, 2001, pp. 867{879. Original Russian Text Copyright c 2001 by Abrashin, Egorov, Zhadaeva. NUMERICAL METHODS On the Convergence Rate of Additive Iterative Methods V. N. Abrashin, A.A.Egorov,and N. G. Zhadaeva Institute for Mathematics, National Academy of Sciences, Minsk, Belarus Belarussian State University, Minsk, Belarus Received March 1, 2001 INTRODUCTION The present paper continues the studies [1{4] of applications of the many-component alternat- ing direction method to stationary boundary value problems of mathematical physics. It is well known [5, 6] that most iterative nite-di erence schemes are based on the reduction of a station- ary equation with a self-adjoint positive de nite operator to the corresponding evolution equation. In this connection, economical iterative schemes based on an additive representation of the original operator are most interesting. Such methods include the classical iterative alternating direction method [5, 6], studied in detail for the case of discrete analogs of elliptic boundary value problems with separated variables and with a two-component decomposition. Economical factorized iterative schemes [5, 6], which require the pairwise commutativity of the decomposition operators, are used in the case of a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the Convergence Rate of Additive Iterative Methods

Abrashin, V.; Egorov, A.; Zhadaeva, N.
Differential Equations , Volume 37 (7) – Oct 12, 2004
Download PDF
14 pages

Loading next page...
 
/lp/springer-journals/on-the-convergence-rate-of-additive-iterative-methods-8dg28TdTp6

References (1)

Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1011968202551
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 7, 2001, pp. 909{922. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 7, 2001, pp. 867{879. Original Russian Text Copyright c 2001 by Abrashin, Egorov, Zhadaeva. NUMERICAL METHODS On the Convergence Rate of Additive Iterative Methods V. N. Abrashin, A.A.Egorov,and N. G. Zhadaeva Institute for Mathematics, National Academy of Sciences, Minsk, Belarus Belarussian State University, Minsk, Belarus Received March 1, 2001 INTRODUCTION The present paper continues the studies [1{4] of applications of the many-component alternat- ing direction method to stationary boundary value problems of mathematical physics. It is well known [5, 6] that most iterative nite-di erence schemes are based on the reduction of a station- ary equation with a self-adjoint positive de nite operator to the corresponding evolution equation. In this connection, economical iterative schemes based on an additive representation of the original operator are most interesting. Such methods include the classical iterative alternating direction method [5, 6], studied in detail for the case of discrete analogs of elliptic boundary value problems with separated variables and with a two-component decomposition. Economical factorized iterative schemes [5, 6], which require the pairwise commutativity of the decomposition operators, are used in the case of a

Journal

Differential Equations – Springer Journals

Published: Oct 12, 2004

There are no references for this article.