, Volume 22, Issue 4, pp 487-502

A weighted pseudoinverse, generalized singular values, and constrained least squares problems

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Abstract

The weighted pseudoinverse providing the minimum semi-norm solution of the weighted linear least squares problem is studied. It is shown that it has properties analogous to those of the Moore-Penrose pseudoinverse. The relation between the weighted pseudoinverse and generalized singular values is explained. The weighted pseudoinverse theory is used to analyse least squares problems with linear and quadratic constraints. A numerical algorithm for the computation of the weighted pseudoinverse is briefly described.

This work was supported in part by the Swedish Institute for Applied Mathematics.