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Third-Order Iterative Regularization for Monotone Equations in a Hilbert Space

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Abstract

For a solvable nonlinear operator equation in a Hilbert space with a monotone hemicontinuous bounded operator, an iterative regularized method is constructed that is linear with respect to difference quotients of the first, second, and third orders. The coefficients in the equation determining the method are not constant and are selected in a special way. Conditions are established for the strong convergence of solutions produced by this method to the normal solution to the original equations. For solutions of inequalities of the second and third orders, upper bounds are derived that play an important role when proving the method convergence.

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Authors and Affiliations

  1. Alekseev Nizhny Novgorod State Technical University, Nizhny Novgorod, 603600, Russia

    I. P. Ryazantseva

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  1. I. P. Ryazantseva
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Correspondence to I. P. Ryazantseva.

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Translated by V. Potapchouck

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Ryazantseva, I.P. Third-Order Iterative Regularization for Monotone Equations in a Hilbert Space. Diff Equat 56, 392–405 (2020). https://doi.org/10.1134/S0012266120030118

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  • DOI: https://doi.org/10.1134/S0012266120030118

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