F. Arandiga et al., FAST MULTIRESOLUTION ALGORITHMS FOR SOLVING LINEAR-EQUATIONS - A COMPARATIVE-STUDY, SIAM journal on scientific computing, 16(3), 1995, pp. 581-600
In [G. Beylkin, R. Coifman, and V. Rokhlin, Comm. Pure Appl. Math., XL
IV (1991), pp. 141-183] and [B. Engquist, S. Osher, and S. Zhong, SIAM
J. Sci. Comput., 15 (1994), pp. 755-775], orthonormal wavelet basis a
nd the multiscale analysis they define are used as building blocks in
the design of algorithms for the rapid numerical application of a numb
er of linear operators to arbitrary vectors. The algorithms may be vie
wed as a method for converting (whenever possible) dense matrices to s
parse form. We use the discrete multiresolution analysis described by
Harten in [J. Appl. Numer. Math., 12 (1993), pp. 153-193] as the build
ing block in the algorithms and compare their performance with the wav
elet-based ones. Computationally, both techniques give comparable resu
lts.