Authors
Jinbiao Wu, Young-Ju Lee, Jinchao Xu, Ludmil Zikatanov
Publication date
2008/11/1
Journal
Journal of Computational Mathematics
Pages
797-815
Publisher
Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences
Description
The convergence analysis on the general iterative methods for the symmetric and positive semidefinite problems is presented in this paper. First, formulated are refined necessary and sufficient conditions for the energy norm convergence for iterative methods. Some illustrative examples for the conditions are also provided. The sharp convergence rate identity for the Gauss-Seidel method for the semidefinite system is obtained relying only on the pure matrix manipulations which guides us to obtain the convergence rate identity for the general successive subspace correction methods. The convergence rate identity for the successive subspace correction methods is obtained under the new conditions that the local correction schemes possess the local energy norm convergence. A convergence rate estimate is then derived in terms of the exact subspace solvers and the parameters that appear in the conditions. The …
Total citations
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Scholar articles
J Wu, YJ Lee, J Xu, L Zikatanov - Journal of Computational Mathematics, 2008