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Ukrainian Mathematical Journal

, Volume 59, Issue 9, pp 1417–1440 | Cite as

Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods

  • I. V. Sergienko
  • E. F. Galba
  • V. S. Deineka
Article

Abstract

We obtain expansions of weighted pseudoinverse matrices with singular weights into matrix power products with negative exponents and arbitrary positive parameters. We show that the rate of convergence of these expansions depends on a parameter. On the basis of the proposed expansions, we construct and investigate iteration methods with quadratic rate of convergence for the calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions. Iteration methods for the calculation of weighted normal pseudosolutions are adapted to the solution of least-squares problems with constraints.

Keywords

Iteration Process Singular Weight Weighted Normal Pseudosolution Weighted Pseudoinverse Matrice Matrix Power Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • I. V. Sergienko
    • 1
  • E. F. Galba
    • 1
  • V. S. Deineka
    • 1
  1. 1.Institute of CyberneticsUkrainian National Academy of SciencesKiev

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