Updating the QR factorization and the least squares problem

Hammarling, Sven and Lucas, Craig (2008) Updating the QR factorization and the least squares problem. [MIMS Preprint]

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Abstract

In this paper we treat the problem of updating the QR factorization, with applications to the least squares problem. Algorithms are presented that compute the factorization A1 = Q1 R1, where A1 is the matrix A = QR after it has had a number of rows or columns added or deleted. This is achieved by updating the factors Q and R, and we show this can be much faster than computing the factorization of A1 from scratch. We consider algorithms that exploit the Level 3 BLAS where possible and place no restriction on the dimensions of A or the number of rows and columns added or deleted. For some of our algorithms we present Fortran 77 LAPACK-style code and show the backward error of our updated factors is comparable to the error bounds of the QR factorization of A1.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Sven Hammarling
Date Deposited: 14 Nov 2008
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1192

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