Geodesic
On continuous regularization method for a constrained pseudoinverse problem with additional restrictions on input operators
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 1, pp. 106-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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A two-parameter continuous method of regularization is considered for a constrained pseudoinverse problem with generalized complementarity of the input operators. This method is based on stabilization of the solutions of differential equations in the Hilbert space. The already known general convergence conditions are specified. The major obtained result is that the parameter functions proved to be independent from each other. The stability of the method is established in the class of all possible constrained disturbances. A one-parameter continuous method of regularization is studied for the special case of the problem with additional input operators.
Keywords: normal constrained pseudosolution, operator equation, Hilbert space, constrained pseudoinverse problem, continuous method of regularization, generalized complementarity condition of operators, complementarity condition of operators. 
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     title = {On continuous regularization method for a~constrained pseudoinverse problem with additional restrictions on input operators},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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R. A. Shafiev; E. A. Bondar; I. Yu. Yastrebova. On continuous regularization method for a constrained pseudoinverse problem with additional restrictions on input operators. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 1, pp. 106-116. http://geodesic.mathdoc.fr/item/UZKU_2016_158_1_a7/

[1] Vainikko G. M., Veretennikov A. Yu., Iterative Procedures in Ill-Posed Problems, Nauka, Moscow, 1986, 181 pp. (In Russian) | MR

[2] Vasin V. V., Ageev A. L., Incorrect Problems with Priori Information, Nauka, Yekaternburg, 1993, 261 pp. (In Russian) | MR

[3] Bondar E. A., Shafiev R. A., “A continuous method for the solution of the bound pseudoinversion problem”, Vestn. Nizhegorod. Univ. im. N. I. Lobachevskogo. Ser. Mat., 2006, no. 1, pt. 4, 4–14 (In Russian)

[4] Shafiev R. A., Pseudoinversion of Operators and Some Applications, Elm, Baku, 1989, 152 pp. (In Russian) | MR

[5] Morozov V. A., Regular Methods for Solving Ill-Posed Problems, Nauka, Moscow, 1987, 360 pp. (In Russian) | MR

[6] Alber Ya. I., “A continuous regularization of linear operators equations in Hilbert spaces”, Mat. Zametki, 4:5 (1968), 503–509 (In Russian) | MR | Zbl

[7] Vasil'ev F. P., Methods for Solving Extremal Problems, Nauka, Moscow, 1981, 400 pp. (In Russian) | MR

[8] Trenogin V. A., Functional Analysis, FIZMATLIT, Moscow, 2007, 488 pp. (In Russian)