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Nonlinear multiscale decompositions: The approach of A. Harten. (English) Zbl 0952.65015
Data-dependent interpolatory techniques can be used in the reconstruction step of a multiresolution scheme designed “à la Harten”. In this paper the authors analyze the class of Essentially Non-Oscillatory (ENO) interpolatory techniques described by A. Harten, B. Engquist, S. Osher and S. Chakravarthy [J. Comput. Phys. 71, 231-303 (1987; Zbl 0652.65067)], and their potential to improve the compression capabilities of multiresolution schemes. This paper is almost self-contained, which turns it into a review of ENO techniques as well as of Harten’s framework for multiresolution decompositions.

MSC:
65D05 Numerical interpolation
65T60 Numerical methods for wavelets
41A05 Interpolation in approximation theory
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