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Titre du document / Document title

Finding the orthogonal projection of a point onto an affine subspace

Auteur(s) / Author(s)

PLESNIK Jan (1) ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

(1) Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 84248 Bratislava, SLOVAQUIE

Résumé / Abstract

A simple method is proposed to find the orthogonal projection of a given point to the solution set of a system of linear equations. This is also a direct method for solving systems of linear equations. The output of the method is either the projection or inconsistency of the system. Moreover, in the process also linearly dependent equations are recognized. This paper is constrained for giving theoretical foundations, computational complexity and some numerical experiments with dense matrices although the method allows to employ sparsity. The raw method could not compete with best software packages in solving linear equations for general matrices, but it was competitive in finding projections for matrices with small number of rows relative to the number of columns.

Revue / Journal Title

Linear algebra and its applications    ISSN  0024-3795   CODEN LAAPAW 

Source / Source

2007, vol. 422, no2-3, pp. 455-470 [16 page(s) (article)] (30 ref.)

Langue / Language

Anglais
Revue : Anglais

Editeur / Publisher

Elsevier, Amsterdam, PAYS-BAS  (1968) (Revue)

Mots-clés anglais / English Keywords

Linear equation

;

Software package

;

Computational complexity

;

Projection method

;

Direct method

;

Equation system

;

Linear system

;

Vector space

;

Orthogonal projection

;

Mots-clés français / French Keywords

Equation linéaire

;

Progiciel

;

Complexité calcul

;

Méthode projection

;

Méthode directe

;

Système équation

;

Système linéaire

;

Espace vectoriel

;

Projection orthogonale

;

Mots-clés espagnols / Spanish Keywords

Ecuación lineal

;

Paquete programa

;

Complejidad computación

;

Método proyección

;

Método directo

;

Sistema ecuación

;

Sistema lineal

;

Espacio vectorial

;

Proyección ortogonal

;

Mots-clés d'auteur / Author Keywords

15A06; 15A03; 15A09; 65F05; 65P50,65Y20

;

Orthogonal projection; Linear equations

;

Localisation / Location

INIST-CNRS, Cote INIST : 14246, 35400014692546.0080

Nº notice refdoc (ud4) : 18593975



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