Wavelet Interpolation and Approximate Solutions of Elliptic Partial Diierential Equations
نویسندگان
چکیده
The paper formulates and proves a second order interpolation result for square-integrable functions by means of locally nite series of Daubechies' wavelets. Sample values of a suuciently smooth function can be used as coeecients of a wavelet expansion at a ne scale, and the corresponding wavelet interpolation function converges in Sobolev norms of rst order to the original function. This has applications to wavelet-Galerkin numerical solutions of elliptic partial diierential equations.
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