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Perturbation theory for generalized and constrained linear least squares
Author(s) -
Gulliksson Mårten,
Wedin PerÅke
Publication year - 2000
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/1099-1506(200005)7:4<181::aid-nla193>3.0.co;2-d
Subject(s) - perturbation (astronomy) , mathematics , rank (graph theory) , linear least squares , least squares function approximation , iteratively reweighted least squares , non linear least squares , explained sum of squares , combinatorics , linear model , statistics , physics , quantum mechanics , estimator
The perturbation analysis of weighted and constrained rank‐deficient linear least squares is difficult without the use of the augmented system of equations. In this paper a general form of the augmented system is used to get simple perturbation identities and perturbation bounds for the general linear least squares problem both for the full‐rank and rank‐deficient problem. Perturbation identities for the rank‐deficient weighted and constrained case are found as a special case. Interesting perturbation bounds and condition numbers are derived that may be useful when considering the stability of a solution of the rank‐deficient general least squares problem. Copyright © 2000 John Wiley & Sons, Ltd.