Iterative methods with different rates of convergence for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights

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:
2004

Citing 4
Cited 3

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Iterative methods for calculating a weighted pseudoinverse

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

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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

The authors develop and analyze iterative methods with different (linear, quadratic, or of p (p驴2) order) rates of convergence. The methods are used to calculate weighted pseudoinverse matrices with positive defined weights. To find weighted normal pseudosolutions with positive defined weights, iterative methods with a quadratic rate of convergence are developed and analyzed. The iterative methods for calculation of weighted normal pseudosolutions are used to solve least-square problems with constraints.