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Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

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Abstract

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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Authors and Affiliations

  1. Mari State University, pl. Lenina 1, Ioshkar-Ola, 424001, Russia

    M. Yu. Kokurin

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  1. M. Yu. Kokurin
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Correspondence to M. Yu. Kokurin.

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Original Russian Text © M.Yu. Kokurin, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 11, pp. 1883–1892.

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Kokurin, M.Y. Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators. Comput. Math. and Math. Phys. 50, 1783–1792 (2010). https://doi.org/10.1134/S0965542510110023

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  • DOI: https://doi.org/10.1134/S0965542510110023

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