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Improvement of Incomplete Factorizations by a Sparse Secant Method.

Please always quote using this URN: urn:nbn:de:0297-zib-401
  • In the present paper, the improvement of an incomplete factorization of a non-symmetric matrix A is discussed. Starting from the ideas of sparsity preserving quasi-Newton methods, an algorithm is developed which improves the approximation of A by the incomplete factorization maintaining the sparsity structure of the matrices. No renumbering of the unknowns or the admittance of additional fill-in is necessary. The linear convergence of the algorithm is proved under the assumption, that $ L $ and $ U $* have the same sparsity structure and an incomplete factorization with some reasonable approximation property exits. In combination with this algorithm, the method of incomplete factorization and its several modifications are applicable to a wider class of problems with improved convergence qualities. This is shown by a numerical example. {\bf Key Words:} non-symmetric linear system, sparse secant method, incomplete factorization. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20, 65N30.

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Metadaten
Author:Artur Walter
Document Type:ZIB-Report
Tag:incomplete factorization; non-symmetric linear systems; sparse secant method
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N20 Ill-posed problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:1990/11/19
Series (Serial Number):ZIB-Report (SC-90-12)
ZIB-Reportnumber:SC-90-12
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