Wavelet methods in numerical analysis

A Cohen - Handbook of numerical analysis, 2000 - Elsevier
Publisher Summary This chapter explains basic examples of wavelet methods in numerical
analysis. It introduces the approximations and shows show the way they are related to …

Adaptive wavelet methods II—beyond the elliptic case

Dahmen, DeVore - Foundations of Computational Mathematics, 2002 - Springer
This paper is concerned with the design and analysis of adaptive wavelet methods for
systems of operator equations. Its main accomplishment is to extend the range of …

Adaptive wavelet methods for solving operator equations: an overview

R Stevenson - … , Nonlinear and Adaptive Approximation: Dedicated to …, 2009 - Springer
Abstract In [Math. Comp, 70 (2001), 27–75] and [Found. Comput. Math., 2 (3)(2002), 203–
245], Cohen, Dahmen and DeVore introduced adaptive wavelet methods for solving …

The wavelet element method: part I. construction and analysis

C Canuto, A Tabacco, K Urban - Applied and Computational Harmonic …, 1999 - Elsevier
The Wavelet Element Method (WEM) combines biorthogonal wavelet systems with the
philosophy of Spectral Element Methods in order to obtain a biorthogonal wavelet system on …

Wavelets on manifolds I: Construction and domain decomposition

W Dahmen, R Schneider - SIAM Journal on Mathematical Analysis, 1999 - SIAM
The potential of wavelets as a discretization tool for the numerical treatment of operator
equations hinges on the validity of norm equivalences for Besov or Sobolev spaces in terms …

Compression techniques for boundary integral equations---asymptotically optimal complexity estimates

W Dahmen, H Harbrecht, R Schneider - SIAM journal on numerical analysis, 2006 - SIAM
Matrix compression techniques in the context of wavelet Galerkin schemes for boundary
integral equations are developed and analyzed that exhibit optimal complexity in the …

[HTML][HTML] Wavelet methods for PDEs—some recent developments

W Dahmen - Journal of Computational and Applied Mathematics, 2001 - Elsevier
This paper is concerned with recent developments of wavelet schemes for the numerical
treatment of operator equations with special emphasis on two issues: adaptive solution …

Adaptive solution of operator equations using wavelet frames

R Stevenson - SIAM Journal on Numerical Analysis, 2003 - SIAM
In" Adaptive wavelet methods II---Beyond the elliptic case" of Cohen, Dahmen, and DeVore
[Found. Comput. Math., 2 (2002), pp. 203--245], an adaptive method has been developed for …

Biorthogonal multiwavelets on the interval: cubic Hermite splines

W Dahmen, B Han, RQ Jia, A Kunoth - Constructive approximation, 2000 - Springer
Starting with Hermite cubic splines as the primal multigenerator, first a dual multigenerator
on R is constructed that consists of continuous functions, has small support, and is exact of …

Adaptive frame methods for elliptic operator equations

S Dahlke, M Fornasier, T Raasch - Advances in Computational …, 2007 - Springer
This paper is concerned with the development of adaptive numerical methods for elliptic
operator equations. We are especially interested in discretization schemes based on frames …