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Multiresolution based on weighted averages of the hat function. II: Nonlinear reconstruction techniques. (English) Zbl 0940.42020
This paper describes and analyzes a class of nonlinear multiresolution schemes for the multiresolution setting which corresponds to discretization by local averages with respect to the hat function. These schemes are based on the essentially-non-oscillatory (ENO) interpolatory procedure described in [A. Harten, B. Engquist, S. Osher and S. Chakravarty, J. Comput. Phys. 71, 231-303 (1987; Zbl 0652.65067)]. The authors show that by allowing the approximation to fit the local nature of the data, one can improve the compression capabilities of the multiresolution algorithms. The question of stability for nonlinear (data-dependent) reconstruction techniques is also addressed. [For Part I see SIAM J. Numer. Anal. 36, No. 1, 160-203 (1998; Zbl 0932.42022)].

MSC:
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
41A15 Spline approximation
41A30 Approximation by other special function classes
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