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Fast multiresolution algorithms for solving linear equations: A comparative study. (English) Zbl 0827.65045

In this interesting paper, the discrete multiresolution analysis introduced by A. Harten in [Appl. Numer. Math. 12, No. 1-3, 153-192 (1993; Zbl 0777.65004)] is used as the building block in the algorithms for converting (whenever possible) dense matrices to sparse form. It seems that Harten’s multiresolution is more natural as well as less restrictive than the usual wavelet transform in most numerical problems. The structure of the compressed matrices and the speed of the algorithms are similar in both cases.
The methods are tested with systems of linear equations obtained by finite difference discretization of hyperbolic/parabolic partial differential equations and by collocation method of a Fredholm integral equation.
Reviewer: M.Tasche (Rostock)

MSC:

65F30 Other matrix algorithms (MSC2010)
65F50 Computational methods for sparse matrices
65T40 Numerical methods for trigonometric approximation and interpolation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65R20 Numerical methods for integral equations
42C15 General harmonic expansions, frames

Citations:

Zbl 0777.65004
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