Accuracy and stability of the null space method for solving the equality constrained least squares problem

Cox, Anthony J. and Higham, Nicholas J. (1999) Accuracy and stability of the null space method for solving the equality constrained least squares problem. BIT Numerical Mathematics, 39 (1). pp. 34-50. ISSN 1572-9125

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Abstract

The null space method is a standard method for solving the linear least squares problem subject to equality constraints (the LSE problem). We show that three variants of the method, including one used in LAPACK that is based on the generalized QR factorization, are numerically stable. We derive two perturbation bounds for the LSE problem: one of standard form that is not attainable, and a bound that yields the condition number of the LSE problem to within a small constant factor. By combining the backward error analysis and perturbation bounds we derive an approximate forward error bound suitable for practical computation. Numerical experiments are given to illustrate the sharpness of this bound.

Item Type:	Article
Uncontrolled Keywords:	Constrained least squares problem - null space method - rounding error analysis - condition number - generalized QR factorization - LAPACK
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:	28 Jun 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/331

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