, Volume 37, Issue 4, pp 961-967

On the weighting method for least squares problems with linear equality constraints

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Abstract

The weighting method for solving a least squares problem with linear equality constraints multiplies the constraints by a large number and appends them to the top of the least squares problem, which is then solved by standard techniques. In this paper we give a new analysis of the method, based on the QR decomposition, that exhibits many features of the algorithm. In particular it suggests a natural criterion for chosing the weighting factor.

Communicated by Åke Björck.
This work was supported in part by the National Science Foundation under grant CCR 95503126.