Sparse Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems.
Please always quote using this URN: urn:nbn:de:0297-zib-483
- A variety of secant methods has been revisited in view of the construction of iterative solvers for large nonsymmetric linear systems $ Ax = b $ stemming from the discretization of convection diffusion equations. In the first section, we tried to approximate $ A ^{-1} $ directly. Since the sparsity structure of A- is not known, additional storage vectors are needed during the iteration. In the next section, an incomplete factorization $ LU $ of $ A $ is the starting point and we tried to improve this easy invertible approximation of $ A $. The update is constructed in such a way that the sparsity structure of $ L $ and $ U $ is maintained. Two different sparsity preserving updates are investigated from theoretical and practical point of view. Numerical experiments on discretized PDEs of convection diffusion type in 2- D with internal layers and on "arbitrary" matrices with symmetric sparsity structure are given. {\bf Key words:} nonsymmetric linear system, sparse secant method, Broyden's method, incomplete factorization.
Author: | Artur Walter |
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Document Type: | ZIB-Report |
Date of first Publication: | 1990/12/20 |
Series (Serial Number): | ZIB-Report (SC-90-20) |
ZIB-Reportnumber: | SC-90-20 |
Published in: | Appeared in: Beauwens, R. et al. (ed.) Iterative Methods on Linear Algebra. Proc. of the IMACS Int. Symp., Brussels, Belgium, 2-4 April, 1991. Amsterdam: Noth-Holland 1992, pp. 449-458 |