Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations

@article{Alpert1993WaveletLikeBF,
title={Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations},
author={Bradley K. Alpert and Gregory Beylkin and Ronald R. Coifman and Vladimir Rokhlin},
journal={SIAM J. Scientific Computing},
year={1993},
volume={14},
pages={159-184}
}

A class of vector-space bases is introduced for the sparse representation of discretiza-tions of integral operators. An operator with a smooth, nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix, to high precision. A method is presented that employs these bases for the numerical solution of second-kind integral equations in time bounded by O(n log 2 n), where n is the number of points in the discretizationâ€¦Â CONTINUE READING