UDC 512.61

Weighted pseudoinversion with singular weights

/ I.V. Sergienko, E.F. Galba // Kibernetika i sistemnyi analiz. — 2016. — Vol. 52, N 5. — P. 56–80.

The paper reviews the development of the theory of weighted pseudoinversion. Weighted pseudoinverse matrices with singular weights are determined and investigated. Theorems of the existence and uniqueness of these matrices are provided. Weighted pseudoinverse matrices with singular weights are related with weighted normal pseudosolutions. Weighted pseudoinverse matrices with singular weights are represented in therms of coefficients of characteristic polynomials of symmetric and symmetrizable matrices. Their expansions in matrix power series and products and limit representations are obtained. Decompositions of weighed pseudoinverse matrices are determined on the basis of the obtained weighed singular decomposition of matrices with singular weights. Figs: 0. Tabl.: 0. Refs: 46 titles.

Keywords:

weighted pseudoinverse matrices with singular weights, matrix power series and products, limit representations of weighted pseudoinverse matrices, weighed singular decomposition of matrices with singular weights.


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Author(s):

Сергиенко Иван Васильевич, академик НАН Украины, директор Института киберентики им. В.М. Глушкова НАН Украины, Киев,
e-mail: aik@public.icyb.kiev.ua

Галба Евгений Федорович, доктор физ.-мат. наук, старший научный сотрудник Института киберентики им. В.М. Глушкова НАН Украины, Киев,
e-mail: e.f.galba@ukr.net