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Condition Number for Weighted Linear Least Squares Problem

Condition Number for Weighted Linear Least Squares Problem

Year:    2007

Journal of Computational Mathematics, Vol. 25 (2007), Iss. 5 : pp. 561–572

Abstract

In this paper, we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem: minxAxb2, where A is an m-by-n (mn) rank deficient matrix. We first derive an explicit expression for the condition number in the weighted Frobenius norm [AT,βb]F of the data A and b, where T is a positive diagonal matrix and β is a positive scalar. We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2007-JCM-8713

Journal of Computational Mathematics, Vol. 25 (2007), Iss. 5 : pp. 561–572

Published online:    2007-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Moore-Penrose inverse Condition number Linear least squares.