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Ukrainian Mathematical Journal

, Volume 70, Issue 6, pp 866–889 | Cite as

Weighted Pseudoinversion with Indefinite Weights

  • N. A. Varenyuk
  • E. F. Galba
  • I. V. Sergienko
  • A. N. Khimich
Article
  • 4 Downloads

We present the definition of weighted pseudoinverse matrices with nondegenerate weights of indefinite sign and study these matrices. The theorems on existence and uniqueness for these matrices are proved. The weighted pseudoinverse matrices with indefinite weights are represented in terms of the coefficients of characteristic polynomials of symmetrized matrices. The decompositions of weighted pseudoinverse matrices into matrix power series and products and their limit representations are obtained. We also propose regularized iterative methods for the determination of these matrices.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • N. A. Varenyuk
    • 1
  • E. F. Galba
    • 1
  • I. V. Sergienko
    • 1
  • A. N. Khimich
    • 1
  1. 1.Institute of CyberneticsUkrainian National Academy of SciencesKievUkraine

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