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 
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/
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     title = {Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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