Expansions of Weighted Pseudoinverses with Mixed Weights into Matrix Power Series and Power Products
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Expansions of weighted pseudoinverses with mixed weights into matrix power series or power products with negative exponents are defined and analyzed. One of these matrices is positive definite and the other is nonsingular and indefinite. Polynomial limit representations of these matrices are obtained. Regularized iterative methods are constructed to evaluate weighted pseudoinverses with mixed weights.
Keywordsweighted pseudoinverses with mixed weights matrix power series and power products limit representations of weighted pseudoinverses regularized iterative methods
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- 9.C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications, Wiley, New York (1971).Google Scholar
- 12.L. S. Pontryagin, “Hermite operators in space with indefinite metrics,” Izv. AN SSSR, Ser. Matematika, No. 8, 243–280 (1944).Google Scholar
- 13.A. I. Mal’tsev, Fundamentals of Linear Algebra [in Russian], Gostekhizdat, Moscow (1948).Google Scholar
- 15.I. Gohberg, P. Lancaster, and L. Rodman, Matrices and Indefinite Scalar Products, Birkhauser, Basel–Boston–Stuttgart (1983).Google Scholar
- 16.T. Ya. Azizov and I. S. Iohvidov, Linear Operators in Spaces with an Indefinite Metric, John Wiley and Sons, Ltd., Chichester (1989).Google Scholar
- 17.P. Lancaster and P. Rozsa, “Eigenvectors of H-self-adjoint matrices,” Z. Angew. Math. und Mech., Vol. 64, No. 9, 439–441 (1984).Google Scholar
- 18.Kh. D. Ikramov, “On algebraic properties of classes of pseudopermutation and H-self-adjoint matrices,” Zhurn. Vych. Mat. Mat. Fiz., Vol. 32, No. 8, 155–169 (1992).Google Scholar
- 19.R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge Univ. Press (2012).Google Scholar
- 22.E. F. Galba, V. S. Deineka, and I. V. Sergienko, “Necessary and sufficient conditions of the existence of one of the variants of weighted singular-value decomposition of matrices with singular weights,” Doklady RAN, Vol. 455, No. 3, 261–264 (2014).Google Scholar
- 26.Y. Wei, “A note on the sensitivity of the solution of the weighted linear least squares problem,” Appl. Math. Comput., Vol. 145, 481–485 (2003).Google Scholar