Wavelet-Galerkin methods: An adapted biorthogonal wavelet basis
type: Item
instance of: scholarly article
title: Wavelet-Galerkin methods: An adapted biorthogonal wavelet basis
zbMATH Open document ID: 0777.34015
DOI: 10.1007/BF01198005
author: Stephan Dahlke
author: Ilona Weinreich
published in: Constructive Approximation
publication date: 1993-12-12T00:00:00Z
review text: The objective of this paper is the construction of a biorthogonal wavelet basis (a function \(f\) is called a wavelet if the scaled (by \(2^ j\), \(j\in Z)\) and integer translated versions of \(f\) form an orthonormal basis of \(L^ 2(\mathbb{R}))\) adapted to a given differential operator. The authors consider some one-dimensional model problems (leading to simple ODEs) to explore the principle possibilities of the adaptation of wavelets to a given problem. A multiresolution analysis approximation such that the resulting wavelets are adapted to simple model problems of the form \(u^{(2m)}(x)=g(x)\) is constructed. It is shown that even for more general elliptic differential operators the condition number of the stiffness matrix is independent of the refinement level.
Mathematics Subject Classification ID: 65J99
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 205300
zbMATH Keywords: biorthogonal wavelet basis
zbMATH Keywords: differential operator
zbMATH Keywords: multiresolution analysis approximation
zbMATH Keywords: elliptic differential operators
zbMATH Keywords: condition number of the stiffness matrix
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 205300