BIT Numerical Mathematics

, Volume 22, Issue 4, pp 487–502

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

  • Lars Eldén
Part II Numerical Mathematics


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 squares pseudoinverse weight matrix constraint generalized singular values 


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Copyright information

© BIT Foundations 1982

Authors and Affiliations

  • Lars Eldén
    • 1
  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden

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