Fast Multiresolution Algorithms for Solving Linear Equations: A Comparative Study
Francesc Aràndiga, Vicente F. Candela, Rosa Donat · SIAM Journal on Scientific Computing · 1995
In [G. Beylkin, R. Coifman, and V. Rokhlin, Comm. Pure Appl. Math., XLIV (1991), PP. 141–183] and [B. Engquist, S. Osher, and S. Zhong, SIAM J. Sci. Comput., 15 (1994), pp. 755–775], orthonormal wavelet basis and the multiscale analysis they define are used as building blocks in the design of algorithms for the rapid numerical application of a number of linear operators to arbitrary vectors. The algorithms may be viewed as a method for converting (whenever possible) dense matrices to sparse form. We use the discrete multiresolution analysis described by Harten in [J. Appl. Numer Math., 12 (1993), pp. 153–193] as the building block in the algorithms and compare their performance with the wavelet-based ones. Computationally, both techniques give comparable results.