Expansions and polynomial limit representations of weighted pseudoinverses

DOI10.1134/S0965542507050016zbMath1231.15006OpenAlexW2046717530MaRDI QIDQ5438126

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

Publication date: 22 January 2008

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542507050016

zbMATH Keywords

iterative methodsconstrained least squares problemsmatrix power seriesweighted normal pseudosolutionsmatrix power productsweighted pseudoinversespolynomial limit representations of weighted pseudoinverses

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09)

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Necessary and sufficient conditions for the existence of weighted singular-valued decompositions of matrices with singular weights ⋮ Weighted pseudoinversion with singular weights ⋮ Existence and uniqueness of weighted pseudoinverses with nonsingular indefinite weights ⋮ Existence and uniqueness of weighted normal pseudosolutions ⋮ Existence and uniqueness theorems in the theory of weighted pseudoinverses with singular weights ⋮ Methods for obtaining reliable solutions to systems of linear algebraic equations ⋮ Numerical solution of some inverse nonstationary thermal conduction problems using pseudoinverses ⋮ Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. I. positive definite weights ⋮ Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. II. singular weights ⋮ Weighted pseudoinversion with indefinite weights ⋮ Expansions of weighted pseudoinverses with mixed weights into matrix power series and power products ⋮ Methods for computing weighted pseudoinverses and weighted normal pseudosolutions with singular weights ⋮ Existence and uniqueness of weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights

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