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On the fast approximation of some nonlinear operators in nonregular wavelet spaces

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Abstract

We focus our attention on the approximation of some nonlinear operators in adapted wavelet spaces. We show the interest of the construction of scaling functions with a large number of zero moments. We present the convergence estimate of an algorithm based on paraproducts for the approximation of nonlinear operators using wavelets connected to scaling functions with zero moments. Numerical tests are performed on univariate examples.

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Authors and Affiliations

  1. ESM2/IRPHE, UMR 6594, La Jetée, Technopôle de Château‐Gombert, F‐13451, Marseille Cedex 20, France

    J. Liandrat

  2. Laboratoire de Mathématiques Fondamentales et Appliquées, Faculté des Sciences de Saint Jérôme, Université Aix–Marseille III, F‐13398, Marseille Cedex 20, France

    Ph. Tchamitchian

  3. LATP, CNRS (UMR6632), Centre de Mathématiques et d'Informatique, Université de Provence, 39, rue Joliot Curie, F‐13453, Marseille Cedex 13, France

    Ph. Tchamitchian

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  1. J. Liandrat
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Liandrat, J., Tchamitchian, P. On the fast approximation of some nonlinear operators in nonregular wavelet spaces. Advances in Computational Mathematics 8, 179–192 (1998). https://doi.org/10.1023/A:1018992129492

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  • DOI: https://doi.org/10.1023/A:1018992129492

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