For one definition of weighted pseudoinversion with singular weights, we establish necessary and sufficient conditions for the existence and uniqueness of a solution of a system of matrix equations. Expansions of weighted pseudoinverse matrices in matrix power series and matrix power products are obtained. A relationship between weighted pseudoinverse matrices the weighted normal pseudosolutions is established. Iterative methods for the calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions are constructed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 80–101, January, 2011.
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Sergienko, I.V., Galba, E.F. & Deineka, V.S. Existence and uniqueness of weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights. Ukr Math J 63, 98–124 (2011). https://doi.org/10.1007/s11253-011-0490-3
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DOI: https://doi.org/10.1007/s11253-011-0490-3