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On algebraic multilevel methods for non-symmetric systems - convergence results

Please always quote using this URN:urn:nbn:de:0296-matheon-4884
  • Here we analyze algebraic multilevel methods applied to non-symmetric M-matrices. We consider two types of multilevel approximate block factorizations. The first one is related to the AMLI method. The second method is the multiplicative counterpart of the AMLI approach which we call multiplicative algebraic multilevel method, the MAMLI method. The MAMLI method is closely related to certain geometric and algebraic multigrid methods like the AMGr method. Although these multilevel methods work very well in practice for many problems, there is not that much known about theoretical convergence properties for non-symmetric problems. Here, we establish convergence results and comparison results between AMLI and MAMLI multilevel methods applied to non-symmetric M-matrices.

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Metadaten
Author:C. Mense, Reinhard Nabben
URN:urn:nbn:de:0296-matheon-4884
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/03/13
Release Date:2008/03/13
Tag:
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F50 Sparse matrices
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N22 Solution of discretized equations [See also 65Fxx, 65Hxx]
Preprint Number:484
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