Iterative method for calculation of weighted pseudoinverse matrices with mixed weights on the basis of their decompositions into matrix power series

1Vareniuk, NA
1Galba, EF
1Sergienko, IV
Tukalevska, NI
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 8:19-25
https://doi.org/10.15407/dopovidi2020.08.019
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 

The decompositions of weighted pseudoinverse matrices with mixed weights (one of the weighted matrices is positive definite, and an other one is nonsingular indefinite) into matrix power series with positive exponents are obtained and investigated. Iterative methods for calculation of weighted pseudoinverse matrices with mixed weights are built and investigated on the basis of obtained expansions of weighted pseudoinverse matrices. Weighted spectral decompositions of symmetrized matrices, properties of these matrices associated with weighted pseudoinverse matrices, and the representation of weighted pseudoinverse matrices with mixed weights in terms of the coefficients of characteristic polynomials of symmetrizable matrices are the mathematical apparatus for constructing and studying the iterative methods for calculating these weighted pseudoinverse matrices. The choice of the iterative parameter is substantiated that provides the convergence of iterative processes. The iterative processes of two types of weighted pseudoinverse matrices are considered.

Keywords: iterative methods, matrix power series, weighted pseudoinverse matrices with indefinite and mixed weights
References: 

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