Geodesic
Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems
Electronic transactions on numerical analysis, Tome 8 (1999), pp. 138-153.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider a construction of efficient preconditioners, using discrete and fast wavelet transforms, for dense and unsymmetric linear systems that arise from boundary elements. The wavelet compression property combined with operator splitting result in much improved preconditioners, in terms of both eigenspectra clustering and inverse approximations, taking the form of band matrices with wrap-around boundaries. With our new nonstandard wavelet transform, the transformed matrix is permuted to band forms. It is shown that, to have band matrices, one has to use a smaller number of wavelet levels. Numerical experiments using the iterative methods of conjugate gradients based on the normal equations (CGN) and generalised minimal residuals (GMRES) are reported.
Classification : 65F10, 65N38, 45E05
Keywords: fast wavelet transforms, dense linear systems, sparse preconditioners, conjugate gradient, boundary elements 
@article{ETNA_1999__8__a1,
     author = {Chen, Ke},
     title = {Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {138--153},
     publisher = {mathdoc},
     volume = {8},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1999__8__a1/}
}
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Chen, Ke. Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems. Electronic transactions on numerical analysis, Tome 8 (1999), pp. 138-153. http://geodesic.mathdoc.fr/item/ETNA_1999__8__a1/