Efficient adaptive operator application on wavelet expansions

Fast computation of adaptive wavelet expansions

In this paper we describe and analyze an algorithm for the fast computation of sparse wavelet coefficient arrays typically arising in adaptive wavelet solvers. The scheme improves on an earlier version from [17] in several respects motivated by recent developments of adaptive wavelet schemes. The new structure of the scheme is shown to enhance its performance while a completely different approa...

Adaptive Wavelet Algorithms for solving operator equations

Nonlinear functionals of wavelet expansions - adaptive reconstruction and fast evaluation

This paper is concerned with the eecient evaluation of nonlinear expressions of wavelet expansions obtained through an adaptive process. In particular, evaluation covers here the computation of inner products of such expressions with wavelets which arise, for instance, in the context of Galerkin or Petrov Galerkin schemes for the solution of diierential equations. The central objective is to de...

Gabor and Wavelet Expansions

This paper is an examination of techniques for obtaining Fourier series-like expansions of finite-energy signals using so-called Gabor and wavelet expansions. These expansions decompose a given signal into time and frequency localized components. The theory of frames in Hilbert spaces is used as a criteria for determining when such expansions are good representations of the signals. Some result...

Truncation Error on Wavelet Sampling Expansions

(see [9] and [10]). Throughout this work, we assume that the function satis®es the following conditions: (i) j …x†j …cons:† jB…x†j=jxj1‡"; where " 0 and jB…x†j is bounded and 1-periodic function on R. (ii) P n2Z …n† eÿin converges absolutely to a function that has no zeros on ‰ÿ ; Š. It is known that conditions (i) and (ii) imply that fK…x; n†; n 2 Zg is a Riesz basis on V , with a unique biort...