Bi-parameter incremental unknowns ADI iterative methods for elliptic problems

Bi-parameter incremental unknowns (IU) alternating directional implicit (ADI) iterative methods are proposed for solving elliptic problems. Condition numbers of the coefficient matrices for these iterative schemes are carefully estimated. Theoretical analysis shows that the condition numbers are red...

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Bibliographic Details
Published in:Numerical algorithms 2012-07, Vol.60 (3), p.483-499
Main Authors: Yang, Aili, Wu, Yujiang, Wu, Yongqing, Ren, Dawei
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Iterative methods
Numeric Computing
Numerical Analysis
Original Paper
Parameters
Theory of Computation
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Summary:Bi-parameter incremental unknowns (IU) alternating directional implicit (ADI) iterative methods are proposed for solving elliptic problems. Condition numbers of the coefficient matrices for these iterative schemes are carefully estimated. Theoretical analysis shows that the condition numbers are reduced significantly by IU method, and the iterative sequences produced by the bi-parameter incremental unknowns ADI methods converge to the unique solution of the linear system if the two parameters belong to a given parameter region. Numerical examples are presented to illustrate the correctness of the theoretical analysis and the effectiveness of the bi-parameter incremental unknowns ADI methods.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-011-9525-y