Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods |
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Authors: | I V Sergienko E F Galba V S Deineka |
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Institution: | (1) Institute of Cybernetics, Ukrainian National Academy of Sciences, Kiev |
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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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1269–1289, September, 2007. |
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