Amat, Sergio; Busquier, Sonia; Negra, Mehdi Adaptive approximation of nonlinear operators. (English) Zbl 1071.65077 Numer. Funct. Anal. Optimization 25, No. 5-6, 397-405 (2004). Second order Taylor approximations of nonlinear operators in Banach spaces are considered. A multiresolution transform corresponding to interpolatory techniques is used for fast application of these approximations. The authors apply data compression to the linear and the bilinear forms that appear on the approximations. An analysis of the error is given and some numerical results are presented. Reviewer: Karel Najzar (Praha) Cited in 41 Documents MSC: 65J15 Numerical solutions to equations with nonlinear operators 65T60 Numerical methods for wavelets 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 47J25 Iterative procedures involving nonlinear operators Keywords:multiresolution; compression; nonlinear operators; Taylor’s approximation; error analysis; Banach spaces; numerical results PDFBibTeX XMLCite \textit{S. Amat} et al., Numer. Funct. Anal. Optim. 25, No. 5--6, 397--405 (2004; Zbl 1071.65077) Full Text: DOI References: [1] DOI: 10.1016/S0096-3003(03)00747-1 · Zbl 1057.65023 · doi:10.1016/S0096-3003(03)00747-1 [2] DOI: 10.1137/0733022 · Zbl 0873.65133 · doi:10.1137/0733022 [3] DOI: 10.1023/A:1019104118012 · Zbl 0952.65015 · doi:10.1023/A:1019104118012 [4] DOI: 10.1002/cpa.3160440202 · Zbl 0722.65022 · doi:10.1002/cpa.3160440202 [5] DOI: 10.1007/BF01889598 · Zbl 0659.65004 · doi:10.1007/BF01889598 [6] DOI: 10.1016/0168-9274(93)90117-A · Zbl 0777.65004 · doi:10.1016/0168-9274(93)90117-A [7] DOI: 10.1137/0733060 · Zbl 0861.65130 · doi:10.1137/0733060 [8] DOI: 10.1006/jath.1996.0054 · Zbl 0883.42024 · doi:10.1006/jath.1996.0054 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.