Solving the indefinite least squares problem by hyperbolic QR factorization

Bojanczyk, Adam and Higham, Nicholas J and Patel, Harikrishna (2003) Solving the indefinite least squares problem by hyperbolic QR factorization. SIAM Journal On Matrix Analysis And Applications, 24 (4). pp. 914-931. ISSN 1095-7162

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Abstract

The indefinite least squares (ILS) problem involves minimizing a certain type of indefinite quadratic form. We develop perturbation theory for the problem and identify a condition number. We describe and analyze a method for solving the ILS problem based on hyperbolic QR factorization. This method has a lower operation count than one recently proposed by Chandrasekaran, Gu, and Sayed that employs both QR and Cholesky factorizations. We give a rounding error analysis of the new method and use the perturbation theory to show that under a reasonable assumption the method is forward stable. Our analysis is quite general and sheds some light on the stability properties of hyperbolic transformations. In our numerical experiments the new method is just as accurate as the method of Chandrasekaran, Gu, and Sayed.

Item Type:	Article
Uncontrolled Keywords:	indefinite least squares problem, downdating, hyperbolic rotation, hyperbolic QR factorization, rounding error analysis, forward stability, perturbation theory, condition number
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:	Ms Lucy van Russelt
Date Deposited:	27 Jun 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/317

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