Result: H2-matrix approximation of integral operators by interpolation

Title:
H2-matrix approximation of integral operators by interpolation
Authors:
HACKBUSCH, Wolfgang, BÖRM, Steffen
Source:
19th Dundee biennial conference on numerical analysis, 26-29 June, 2001, Dundee, Scotland, UKApplied numerical mathematics. 43(1-2):129-143
Publisher Information:
Amsterdam: Elsevier, 2002.
Publication Year:
2002
Physical Description:
print, 9 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Théorie des opérateurs, Operator theory, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Approximation numérique, Numerical approximation, Aproximación numérica, Calcul erreur, Error analysis, Cálculo error, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Espace n dimensions, Multidimensional space, Espacio n dimensiones, Fonction noyau, Kernel function, Función núcleo, Interpolation polynomiale, Polynomial interpolation, Interpolación polinomial, Méthode discrétisation, Discretization method, Método discretización, Méthode panneau, Panel method, Método panel, Méthode partition, Partition method, Método partición, Opérateur intégral, Integral operator, Operador integral, Simulation numérique, Numerical simulation, Simulación numérica, Sous variété, Submanifold, Subvariedad, Algorithme amas, Cluster algorithm, Approximation matricielle, Matrix approximation, Matrice H, H matrix
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Max-Planck-Institut Mathematik in den Naturwissenschaften, Inselstr. 22-26, 04103 Leipzig, Germany
ISSN:
0168-9274
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=13935584
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.13935584
Database:
PASCAL Archive

Further Information

Typical panel clustering methods for the fast evaluation of integral operators are based on the Taylor expansion of the kernel function and therefore usually require the user to implement the evaluation of the derivatives of this function up to an arbitrary degree. We propose an alternative approach that replaces the Taylor expansion by simple polynomial interpolation. By applying the interpolation idea to the approximating polynomials on different levels of the cluster tree, the matrix vector multiplication can be performed in only O(npd) operations for a polynomial order of p and an n-dimensional trial space. The main advantage of our method, compared to other methods, is its simplicity: Only pointwise evaluations of the kernel and of simple polynomials have to be implemented.