2017
Том 69
№ 9

All Issues

Existence and uniqueness of weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights

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

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Abstract

For one of definitions of weighted pseudoinversion with singular weights, necessary and sufficient conditions for the existence and uniqueness are obtained. Expansions of weighted pseudoinverse matrices in matrix power series and matrix power products are obtained. Relationship is established between the weighted pseudoinverse matrices and the weighted normal pseudosolutions. Iterative methods for the calculation of both weighted pseudoinverse matrices and weighted normal pseudosolutions are constructed.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 1, pp 98-124.

Citation Example: Deineka V. S., Galba E. F., Sergienko I. V. Existence and uniqueness of weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights // Ukr. Mat. Zh. - 2011. - 63, № 1. - pp. 80-101.

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