Paper Info
Title
Componentwise perturbation analyses for the QR factorization
Abstract
Summary.   This paper gives componentwise perturbation analyses for Q and R in the QR factorization A=QR, , R upper triangular, for a given real $m\times n$ matrix A of rank n. Such specific analyses are important for example when the columns of A are badly scaled. First order perturbation bounds are given for both Q and R. The analyses more accurately reflect the sensitivity of the problem than previous such results. The condition number for R is bounded for a fixed n when the standard column pivoting strategy is used. This strategy also tends to improve the condition of Q, so usually the computed Q and R will both have higher accuracy when we use the standard column pivoting strategy. Practical condition estimators are derived. The assumptions on the form of the perturbation are explained and extended. Weaker rigorous bounds are also given.
Year
DOI
Venue
2001
10.1007/PL00005447
Numerische Mathematik
Keywords
Field
DocType
first order,condition number,qr factorization
Condition number,M-matrix,Upper and lower bounds,Mathematical analysis,Matrix (mathematics),Factorization,Triangular matrix,Mathematics,QR decomposition,Bounded function
Journal
Volume
Issue
ISSN
88
2
0029-599X
Citations 
PageRank 
References 
12
1.16
0
Authors
2
Name
Order
Citations
PageRank
Xiao-Wen Chang120824.85
Christopher C. Paige2724608.16