Abstract
Necessary and sufficient conditions for the existence and uniqueness of weighted pseudoinverses with singular weights are obtained. Pseudoinverses are expanded into matrix power series and power products. A relationship is found between weighted pseudoinverses and weighted normal pseudosolutions, and iterative methods are established for calculating pseudoinverses and pseudosolutions.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 14–33, January–February 2011.
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Sergienko, I.V., Galba, Y.F. & Deineka, V.S. Existence and uniqueness theorems in the theory of weighted pseudoinverses with singular weights. Cybern Syst Anal 47, 11–28 (2011). https://doi.org/10.1007/s10559-011-9286-6
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DOI: https://doi.org/10.1007/s10559-011-9286-6