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A weighted pseudoinverse, generalized singular values, and constrained least squares problems
 Lars Eldén
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The weighted pseudoinverse providing the minimum seminorm solution of the weighted linear least squares problem is studied. It is shown that it has properties analogous to those of the MoorePenrose 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.
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 Title
 A weighted pseudoinverse, generalized singular values, and constrained least squares problems
 Journal

BIT Numerical Mathematics
Volume 22, Issue 4 , pp 487502
 Cover Date
 19821201
 DOI
 10.1007/BF01934412
 Print ISSN
 00063835
 Online ISSN
 15729125
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Least squares
 pseudoinverse
 weight matrix
 constraint
 generalized singular values
 Industry Sectors
 Authors

 Lars Eldén ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Linköping University, S58183, Linköping, Sweden