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

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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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     author = {M. Yu. Kokurin},
     title = {Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1883--1892},
     publisher = {mathdoc},
     volume = {50},
     number = {11},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a1/}
}
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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/