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

Authors:
I. V. Sergienko;E. 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:
2008

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Abstract

The paper reviews studies on the representations and expansions of weighted pseudoinverse matrices with positive semidefinite weights and on the construction of iterative methods and regularized problems for the calculation of weighted pseudoinverses and weighted normal pseudosolutions based on these representations and expansions. The use of these methods to solve constrained least squares problems is examined.