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On Frobenius normwise condition numbers for Moore–Penrose inverse and linear least‐squares problems
Author(s) -
Diao Huaian,
Wei Yimin
Publication year - 2007
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.540
Subject(s) - mathematics , rank (graph theory) , condition number , inverse , least squares function approximation , computation , moore–penrose pseudoinverse , linear least squares , combinatorics , statistics , linear model , algorithm , geometry , eigenvalues and eigenvectors , physics , quantum mechanics , estimator
Condition numbers play an important role in numerical analysis. Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using norms. In this paper, we give explicit, computable expressions depending on the data, for the normwise condition numbers for the computation of the Moore–Penrose inverse as well as for the solutions of linear least‐squares problems with full‐column rank. Copyright © 2007 John Wiley & Sons, Ltd.