Convergence estimates for multigrid algorithms

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To estimate convergence of the multigrid algorithms, we need some assumptions on smoothers. The assumptions for typical smoothers are well analyzed in the multigrid literature [1,2]. However, numerical evidence shows that Kaczmarz smoother does not satisfy above assumptions. Thus, we introduce a weaker condition which is satisfied by Kaczmarz smoother as well as Jacobi and Gauss-Seidel smoother. Under these weaker assumptions, we show that the convergence factor of V-cycle multigrid algorithm is delta = 1-1/(C(j-1)). These assumptions for Kaczmarz smoother are verified by numerical experiment.
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Issue Date
1997
Language
English
Article Type
Article
Keywords

V-CYCLE

Citation

COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.34, pp.15 - 22

ISSN
0898-1221
URI
http://hdl.handle.net/10203/21474
Appears in Collection
MA-Journal Papers(저널논문)
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