On the Accuracy of the Karlson--Waldén Estimate of the Backward Error for Linear Least Squares Problems

Autor:	Serge Gratton, Pavel Jiránek, David Titley-Peloquin
Rok vydání:	2012
Předmět:	Recursive least squares filter Mathematical optimization Non-linear least squares Applied mathematics Generalized least squares Total least squares Residual Least squares Analysis Projection (linear algebra) Linear least squares Mathematics
Zdroj:	SIAM Journal on Matrix Analysis and Applications. 33:822-836
ISSN:	1095-7162 0895-4798
Popis:	We consider the backward error associated with a given approximate solution of a linear least squares problem. The backward error can be very expensive to compute, as it involves the minimal singular value of a certain matrix that depends on the problem data and the approximate solution. An estimate based on a regularized projection of the residual vector has been proposed in the literature and analyzed by several authors. Although numerical experiments in the literature suggest that it is a reliable estimate of the backward error for any given approximate least squares solution, to date no satisfactory explanation for this behavior had been found. We derive new bounds which confirm this experimental observation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::564170e442babc86562e219ac4b765d0 https://doi.org/10.1137/110825467 Zobrazit plný text záznamu