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: $\min_x \|Ax-b\|_2$, where $A$ is an $m$-by-$n$ ($m \ge n$) rank deficient matrix. We first derive an explicit expression for the condition number in the weighted Frobenius norm $\|\left[AT, \beta b\right] \|_F$ of the data $A$ and $b$, where $T$ is a positive diagonal matrix and $\beta$ 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.