2017
Том 69
№ 6

All Issues

Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods

Deineka V. S., Galba E. F., Sergienko I. V.

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Abstract

We obtain expansions of weighted pseudoinverse matrices with singular weights into matrix power products with negative exponents and arbitrary positive parameters. We show that the rate of convergence of these expansions depends on a parameter. On the basis of the proposed expansions, we construct and investigate iteration methods with quadratic rate of convergence for the calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions. Iteration methods for the calculation of weighted normal pseudosolutions are adapted to the solution of least-squares problems with constraints.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 9, pp 1417-1440.

Citation Example: Deineka V. S., Galba E. F., Sergienko I. V. Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods // Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1269–1289.

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