Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces

Nils Reich

Displaying similar documents to “Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces”

Approximate multiplication in adaptive wavelet methods

Dana Černá, Václav Finěk (2013)

Open Mathematics

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Cohen, Dahmen and DeVore designed in [Adaptive wavelet methods for elliptic operator equations: convergence rates, Math. Comp., 2001, 70(233), 27–75] and [Adaptive wavelet methods II¶beyond the elliptic case, Found. Comput. Math., 2002, 2(3), 203–245] a general concept for solving operator equations. Its essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l 2-problem, finding the convergent iteration process for the l 2-problem...

Discrete differential operators in multidimensional Haar wavelet spaces.

Cattani, Carlo, Sánchez Ruiz, Luis M. (2004)

International Journal of Mathematics and Mathematical Sciences

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Best -term approximation in electronic structure calculations I. One-electron reduced density matrix

Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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We discuss best -term approximation spaces for one-electron wavefunctions $φ_{i}$ and reduced density matrices emerging from Hartree-Fock and density functional theory. The approximation spaces $A_{q}^{α} (H^{1})$ for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted $ℓ_{q}$ spaces of wavelet coefficients to proof that both $φ_{i}$ and are in $A_{q}^{α} (H^{1})$ for all $α > 0$ with $α = \frac{1}{q} - \frac{1}{2}$ . Our proof is based...

Embedding and a priori wavelet-adaptivity for Dirichlet problems

Andreas Rieder (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

evaluation of the $Ω_{j, k}^{m, n} (x)$ coefficients for PDE solving by wavelet-Galerkin approximation.

Popovici, Constantin I. (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Haar wavelets method for solving Pocklington's integral equation

M. Shamsi, Mohsen Razzaghi, J. Nazarzadeh, Masoud Shafiee (2004)

Kybernetika

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A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning...

Wavelet techniques for pointwise regularity

Stéphane Jaffard (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let $E$ be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with $E$ , and denoted by $C_{E}^{α} (x_{0})$ . We show how properties of $E$ are transferred into properties of $C_{E}^{α} (x_{0})$ . Applications are given in multifractal analysis.