|
Abstract : |
The paper formulates and proves a second order interpolation result for square-integrable functions by means of locally finite series of Daubechies ' wavelets. Sample values of a sufficiently smooth function can be used as coefficients of a wavelet expansion at a fine scale, and the corresponding wavelet interpolation function converges in Sobolev norms of first order to the original function. This has applications to wavelet-Galerkin numerical solutions of elliptic partial differential equations. 1, |
