Skip to main content
Article thumbnail
Location of Repository

Accuracy and Stability of the Null Space Method for Solving the Equality Constrained Least Squares Problem

By Anthony J. Cox and Nicholas J. Higham

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. Key words: Constrained least squares problem, null space method, rounding error analysis, condition number, generalized QR factorization, LAPAC

Year: 1999
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.3531
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.maths.man.ac.uk/~hi... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.