Limiting Representations of Weighted Pseudoinverse Matrices with Positive Definite Weights. Problem Regularization

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 aik@public.icyb.kiev.ua;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 dejneka@public.icyb.kiev.ua
Venue:
Cybernetics and Systems Analysis
Year:
2003

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Abstract

Limiting representations for weighted pseudoinverse matrices with positive definite weights are derived. It is shown that regularized problems can be constructed based on such limiting representations intended for evaluation of weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights. The results obtained, concerning regularization of problems on evaluation of weighted normal pseudosolutions, are employed for regularization of least-squares problems with constraints.