21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Matthias Bollhöfer, Fri, 11.00-11.30 Previous Contents Next  
  Inverse-Based Algebraic Multilevel Factorizations Methods
Matthias Bollhöfer (TU Berlin)

We discuss an algebraic multilevel factorization approach for the solution of large sparse linear systems. The objective of this approach is to detect a submatrix of the original matrix such that its inverse is approximately sparse. One possibility could be to construct an adapted sparse approximate inverse of the associated leading submatrix, another approach consists of directly constructing an incomplete LU decomposition such that the inverse triangular factors are bounded. From the theoretical point of view this can be interpreted as keeping the approximate triangular factors L and U and their inverses close to each other.

Different strategies will be presented that address the problem of finding a submatrix with sparse approximate inverse.

Successively applied, this leads to an algebraic multilevel hierarchy. Numerical examples will be shown to illustrate the effectiveness of this approach.


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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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