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Properties and least‐squares problems for row extended matrices
Author(s) -
Zhao Lijun,
Hu Xiyan,
Zhang Lei
Publication year - 2010
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/nla.648
Subject(s) - mathematics , perturbation (astronomy) , least squares function approximation , representation (politics) , mathematical optimization , statistics , physics , quantum mechanics , estimator , politics , political science , law
In this paper, we discuss basic properties, a least‐squares problem for row extended matrices and the associated approximation problem. First, we obtain their basic properties by applying their particular structure. Then we derive a general representation of the solutions to the least‐squares problem, and we obtain an expression for the solution to the associated approximation problem. Finally, we provide a perturbation analysis and a perturbation bound for the best approximate solution. The results are illustrated by numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.