Abstract
For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree structure. Applications are found in the field of (adaptive) tensor product solution methods for semilinear operator equations by collocation methods, or after transformations between the interpolet and (bi-) orthogonal wavelet bases, by Galerkin methods.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Schwab, C., Stevenson, R. Fast evaluation of nonlinear functionals of tensor product wavelet expansions. Numer. Math. 119, 765–786 (2011). https://doi.org/10.1007/s00211-011-0397-9
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DOI: https://doi.org/10.1007/s00211-011-0397-9