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Abstract: In recent years application of a discrete wavelet transform (DWT) has become an established tool for the design of preconditioners for smooth, dense matrices, such as those that arise in the solution of certain integral equations. In this paper we consider the higher dimensional case, where the matrix A is not itself smooth, but has a smooth block structure. To precondition such matrices, we use repeated application of a level 1 blockwise DWT to exploit the fact that corresponding entries in... (Update)
Active bibliography (related documents): More All
1.9: Wavelet-Based Preconditioning of Dense Linear Systems - Ford (2001) (Correct)
1.3: An improved DWT-based preconditioner for dense matrix problems - Ford (2002) (Correct)
0.4: On Two Variants of an Algebraic Wavelet Preconditioner - Tony Chan And (2002) (Correct)
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0.0: Unknown - (Correct)
BibTeX entry: (Update)
@misc{ ford-waveletbased,
author = "Judith M. Ford and Ke Chen",
title = "A Wavelet-Based Preconditioning Method for Dense Matrices with Block Structure",
url = "citeseer.ist.psu.edu/755802.html" }
Citations (may not include all citations):525 Iterative Methods for Sparse Linear Systems (context) - Saad - 1996
297 Fast wavelet transforms and numerical algorithms (context) - Beylkin, Coifman et al. - 1991
263 Iterative solution methods (context) - Axelsson - 1996
97 Wavelets and Filter Banks (context) - Strang, Nguyen - 1996
17 A exible inner-outer preconditioned GMRES algorithm (context) - Saad - 1993
13 LU factorization of non-standard forms and direct multiresol.. (context) - Gines, Beylkin et al. - 1998
11 a class of preconditioning methods for dense linear systems .. (context) - Chen - 1998
10 A new wavelet transform preconditioner for iterative solutio.. - Ford, Chen et al. - 2000
7 Discrete wavelet transforms accelerated sparse preconditione.. (context) - Chen - 1999
6 Wavelet-based preconditioners for dense matrices with non-sm.. - Ford, Chen - 2001
4 An algorithm for accelerated computation of DWTPer-based ban.. - Ford, Chen - 2001
4 Two-stage preconditioners using wavelet band splitting and s.. - Chan, Chen - 2000
3 a recursive Schur preconditioner for iterative solution of a.. (context) - Ford, Chen et al.
2 Multiresolution analysis and supercompact multiwavelets (context) - Beam, Warming - 2000
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