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Adaptive approximation of nonlinear operators. (English) Zbl 1071.65077
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.

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
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References:
[1] DOI: 10.1016/S0096-3003(03)00747-1 · Zbl 1057.65023
[2] DOI: 10.1137/0733022 · Zbl 0873.65133
[3] DOI: 10.1023/A:1019104118012 · Zbl 0952.65015
[4] DOI: 10.1002/cpa.3160440202 · Zbl 0722.65022
[5] DOI: 10.1007/BF01889598 · Zbl 0659.65004
[6] DOI: 10.1016/0168-9274(93)90117-A · Zbl 0777.65004
[7] DOI: 10.1137/0733060 · Zbl 0861.65130
[8] DOI: 10.1006/jath.1996.0054 · Zbl 0883.42024
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