BIT Numerical Mathematics

, Volume 22, Issue 4, pp 487–502

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


  • Lars Eldén
    • Department of MathematicsLinköping University
Part II Numerical Mathematics

DOI: 10.1007/BF01934412

Cite this article as:
Eldén, L. BIT (1982) 22: 487. doi:10.1007/BF01934412


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.

Key words

Least squarespseudoinverseweight matrixconstraintgeneralized singular values

Copyright information

© BIT Foundations 1982