Wavelet-based preconditioners for dense matrices
                       with non-smooth local features

                         Judith Ford and Ke Chen

                         Department of Mathematical Sciences,
                         University of Liverpool,
                         Liverpool, L69 7ZL, UK. 

                         Emails: judyford@liv.ac.uk  and  k.chen@liverpool.ac.uk
                         Web: http//www.liv.ac.uk/maths/applied

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Abstract.

We present algorithms for the detection of local non-smooth features within a 
dense matrix and show how, by isolating such features, we are able to use 
wavelet compression to design preconditioners for the corresponding dense linear
system. We illustrate our approach with examples from the solution of 
Elastohydrodynamic Lubrication problems and Boundary Integral Equations.

AMS subject classification: 65F10, 65F50, 76D08, 45E05. 

Key words: Preconditioning, GMRES, wavelet transform, dense matrices, 
           elastohydrodynamic lubrication, boundary integral equations.

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