Published 1993
| Version v1
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Matrices, momenta and quadrature
Creators
- 1. Centre d'Etudes de Limeil-Valenton, Departement de Mathematiques Appliquees, Service Mathematiques et Codes Numeriques, 94195 Villeneuve Saint Georges Cedex (France)
- 2. Computer Science Department, Stanford University, Stanford CA 94305 (United States)
Description
In this paper we study methods to obtain bounds or approximations of elements of a matrix f(A) where A is a symmetric positive definite matrix and f is a smooth function. These methods are based on the use of quadrature rules and the Lanczos algorithm for diagonal elements and the black Lanczos or the non-symmetric Lanczos algorithms for the non-diagonal elements. We give some theoretical results on the behavior of these methods based on results for orthogonal polynomials as well as analytical bounds and numerical experiments on a set of matrices for several functions f. (author)
Abstract (French)
Dans ce papier, nous etudions des methodes permettant d'obtenir des bornes ou des approximations des elements d'une matrice f(A) ou A est une matrice symetrique definie positive et f une fonction suffisamment reguliere. Ces methodes sont basees sur l'utilisation de formules d'integration et sur la methode de Lanczos pour l'estimation des elements diagonaux et sur les methodes de Lanczos non symetrique et de Lanczos par blocs pour les elements non diagonaux. Nous developpons la theorie concernant le comportement de ces methodes en utilisant des resulats sur les polynomes orthogonaux. On obtient egalement des bornes analytiques pour les elements de l'inverse d'une matrice et l'on presente des resultats numeriques sur un ensemble de matrices et pour differentes fonctions f. (auteur)Files
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Additional details
Additional titles
- Original title (French)
- Matrices, moments et quadrature
Publishing Information
- Imprint Pagination
- 61 p.
- Report number
- CEA-N--2727
INIS
- Country of Publication
- France
- Country of Input or Organization
- France
- INIS RN
- 49089255
- Subject category
- S97: MATHEMATICAL METHODS AND COMPUTING;
- Descriptors DEI
- ALGORITHMS; EIGENVALUES; EIGENVECTORS; HERMITE POLYNOMIALS; HILBERT SPACE; INTEGRALS; INTERPOLATION; ITERATIVE METHODS; MATRICES; POISSON EQUATION; QUADRATURES; RECURSION RELATIONS
- Descriptors DEC
- BANACH SPACE; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; MATHEMATICAL LOGIC; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; SPACE
Optional Information
- Notes
- 21 refs.; Available from the INIS Liaison Officer for France, see the INIS website for current contact and E-mail addresses