Geodesic
A finite-dimensional regularized gradient method for solving irregular nonlinear operator equations
Numerical methods and programming, Tome 8 (2007) no. 1, pp. 88-94.

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We construct and study a finite-dimensional iterative process of gradient type for the approximate solution of irregular nonlinear operator equations in a Hilbert space. Convergence properties of the process are studied in the presence of noise in input data. We propose a stopping criterion that ensures to obtain approximate solutions adequate to the level of errors in input data.
Keywords: nonlinear equations, irregular operator, gradient methods, stability, operator equations, regular methods. 
@article{VMP_2007_8_1_a10,
     author = {M. Yu. Kokurin and O. V. Karabanova},
     title = {A finite-dimensional regularized gradient method for solving irregular nonlinear operator equations},
     journal = {Numerical methods and programming},
     pages = {88--94},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a10/}
}
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M. Yu. Kokurin; O. V. Karabanova. A finite-dimensional regularized gradient method for solving irregular nonlinear operator equations. Numerical methods and programming, Tome 8 (2007) no. 1, pp. 88-94. http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a10/