FAST MULTIRESOLUTION ALGORITHMS FOR SOLVING LINEAR-EQUATIONS - A COMPARATIVE-STUDY

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.