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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.61
E.F. Galba,1 I.V. Sergienko2

METHODS FOR COMPUTING WEIGHTED PSEUDOINVERSE MATRICES AND WEIGHTED
NORMAL PSEUDOSOLUTIONS WITH SINGULAR WEIGHTS

Abstract. This paper surveys articles in which direct and iterative methods are constructed and investigated for computing weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights. The considered methods are mainly constructed based on the authors’ articles devoted to the development of the theory of weighted pseudoinversion in the direction of investigating the characteristics of both weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights. This article uses the following results obtained and investigated by the authors: expansions of weighted pseudoinverse matrices into matrix power series and products, limit representations of such matrices, and determination of decompositions of weighted pseudoinverse matrices based on weighted singular decompositions of matrices with singular weights.

Keywords: weighted pseudoinverse matrix with singular weights, weighted normal pseudosolution with singular weights, iterative method, regularized problem.



FULL TEXT

1 V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
e.f.galba@ukr.net.

2 V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
e-mail: aik@publik.icub.kiev.ua.

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