## 2006.153: Accuracy and stability of the null space method for solving the equality constrained least squares problem

2006.153:
Anthony J. Cox and Nicholas J. Higham
(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 |
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Uncontrolled Keywords: | Constrained least squares problem - null space method - rounding error analysis - condition number - generalized QR factorization - LAPACK |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.153 |

Deposited By: | Miss Louise Stait |

Deposited On: | 28 June 2006 |

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