Geodesic
Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1883-1892 Cet article a éte moissonné depuis la source Math-Net.Ru

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A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics. 
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M. Yu. Kokurin. Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1883-1892. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a1/

[1] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Fizmatlit, M., 1995 | MR

[2] Bakushinskii A. B., Kokurin M. Yu., Iteratsionnye metody resheniya nekorrektnykh operatornykh uravnenii s gladkimi operatorami, Editorial URSS, M., 2002

[3] Bakushinsky A., Kokurin M., Iterative methods for approximate solution of inverse problems, Springer, Dordrecht, 2005 | MR

[4] Goryunov A. A., Saskovets A. V., Obratnye zadachi rasseyaniya v akustike, Izd-vo MGU, M., 1989

[5] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[6] Vainikko G. M., Veretennikov A. Yu., Iteratsionnye protsedury v nekorrektnykh zadachakh, Nauka, M., 1986 | MR

[7] Bakushinskii A. B., “Iteratsionnye metody s nechetkoi obratnoi svyazyu dlya resheniya neregulyarnykh operatornykh uravnenii”, Dokl. RAN, 428:5 (2009), 583–585 | MR