Методы вычисления взвешенных псевдообратных матриц и взвешенных нормальных псевдорешений с вырожденными весами / Галба Е. Ф., Сергиенко И. В. (2018)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2018, 54 (3))

Galba E.F., Sergienko I.V.
Methods for computing weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights

The paper surveys articles that construct and investigate direct and iterative methods for computing weighted pseudoinverses and weighted normal pseudosolutions with singular weights. The methods considered in the paper are mainly constructed based on the authors’ articles devoted to the development of the theory of weighted pseudoinversion aimed at investigating the characteristics of both weighted pseudoinverses and weighted normal pseudosolutions with singular weights. The paper uses the following results obtained and investigated by the authors: expansions of weighted pseudoinverses into matrix power series and products, limit representations of such matrices, and determination of decompositions of weighted pseudoinverses based on weighted singular value decompositions of matrices with singular weights. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: iterative method, regularized problem, weighted normal pseudosolutions with singular weights, weighted pseudoinverses with singular weights, Computation theory, Singular value decomposition, Direct and iterative method, Matrix power, Paper surveys, Pseudo-inverses, Pseudo-inversion, regularized problem, Singular weight, Weighted normal pseudosolutions, Iterative methods


Cite:
Galba E.F., Sergienko I.V. (2018). Methods for computing weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights. Cybernetics and Systems Analysis, 54 (3), 65-93. doi: https://doi.org/10.1007/s10559-018-0042-z http://jnas.nbuv.gov.ua/article/UJRN-0000863960 [In Russian].


 

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