Treffer: Numerical stability of orthogonalization methods with a non-standard inner product
Title:
Numerical stability of orthogonalization methods with a non-standard inner product
Source:
BIT (Nordisk Tidskrift for Informationsbehandling). 52(4):1035-1058
Publisher Information:
Dordrecht: Springer, 2012.
Publication Year:
2012
Physical Description:
print, 38 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Analyse mathématique, Mathematical analysis, Analyse fonctionnelle, Functional analysis, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Algorithme, Algorithm, Algoritmo, Algèbre linéaire numérique, Numerical linear algebra, Algebra lineal numérica, Analyse numérique, Numerical analysis, Análisis numérico, Arithmétique intervalle, Interval arithmetic, Aritmética intervalo, Calcul erreur, Error analysis, Cálculo error, Erreur arrondi, Rounding error, Error redondear, Implémentation, Implementation, Implementación, Indice conditionnement, Condition number, Numero de condicionamiento, Matrice définie positive, Positive definite matrix, Matriz definida positiva, Matrice orthogonale, Orthogonal matrix, Matriz ortogonal, Matrice symétrique, Symmetric matrix, Matriz simétrica, Méthode numérique, Numerical method, Método numérico, Méthode stochastique, Stochastic method, Método estocástico, Orthogonalité, Orthogonality, Ortogonalidad, Préconditionnement, Preconditioning, Precondicionamiento, Stabilité numérique, Numerical stability, Estabilidad numérica, 15A12, 46Cxx, 65C20, 65F08, 65F25, 65F35, 65G30, 65G50, 65Gxx, 65K15, Analyse erreur, 15A23, Gram-Schmidt process, Orthogonalization schemes, QR factorization, Rounding error analysis
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07 Prague 8, Czech Republic
Faculty of Mathematics and Information Science, Warsaw University of Technology, PI. Politechniki 1, 00-661 Warsaw, Poland
Institute of Novel Technologies and Applied Informatics, Technical University of Liberec, Halkova 6, 461 17 Liberec, Czech Republic
Faculty of Mathematics and Information Science, Warsaw University of Technology, PI. Politechniki 1, 00-661 Warsaw, Poland
Institute of Novel Technologies and Applied Informatics, Technical University of Liberec, Halkova 6, 461 17 Liberec, Czech Republic
ISSN:
0006-3835
Rights:
Copyright 2015 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
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.26594266
Database:
PASCAL Archive
Weitere Informationen
In this paper we study the numerical properties of several orthogonalization schemes where the inner product is induced by a nontrivial symmetric and positive definite matrix. We analyze the effect of its conditioning on the factorization and the loss of orthogonality between vectors computed in finite precision arithmetic. We consider the implementation based on the backward stable eigendecomposition, modified and classical Gram―Schmidt algorithms, Gram―Schmidt process with re-orthogonalization as well as the implementation motivated by the AINV approximate inverse preconditioner.