Existence and uniqueness theorems in the theory of weighted pseudoinverses with singular weights

Authors:
I. V. Sergienko;Ye. F. Galba;V. S. Deineka
Affiliations:
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2011

Citing 3
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Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. II. Singular weights

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Abstract

Necessary and sufficient conditions for the existence and uniqueness of weighted pseudoinverses with singular weights are obtained. Pseudoinverses are expanded into matrix power series and power products. A relationship is found between weighted pseudoinverses and weighted normal pseudosolutions, and iterative methods are established for calculating pseudoinverses and pseudosolutions.