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Cybernetics and Systems Analysis

, Volume 51, Issue 4, pp 514–528 | Cite as

Weighted Singular Value Decomposition of Matrices with Singular Weights Based on Weighted Orthogonal Transformations

  • I. V. Sergienko
  • E. F. Galba
SYSTEMS ANALYSIS

Abstract

Two variants of weighted singular value decompositions of matrices with singular weights using weighted orthogonal matrices are obtained and analyzed. Based on this singular value decompositions of matrices, decomposition of weighted pseudoinverse matrices with singular weights and decomposition of these matrices into matrix power series and products are obtained. The application of these decompositions is determined.

Keywords

weighted singular value decomposition of matrices with singular weights weighted pseudoinverse matrices with singular weights weighted normal pseudosolutions weighted orthogonal transformations matrix power series matrix power products regularized problems 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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