Series expansion of weighted pseudoinverse matrices and iterative methods for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions

Authors:
I. V. Sergienko;E. F. Galba;V. S. Deineka
Affiliations:
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2006

Citing 0
Cited 3

Expansion of weighted pseudoinverse matrices with positive definite weights into matrix power products. Iterative methods

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Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. I. Positive definite weights

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

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Abstract

Weighted pseudoinverse matrices are expanded into matrix power series with negative exponents and arbitrary positive parameters. Based on this expansion, iterative methods for evaluating weighted pseudoinverse matrices and weighted normal pseudosolutions are designed and analyzed. The iterative methods for weighted normal pseudosolutions are extended to solving constrained least-squares problems.