Geodesic
Iterative processes for nonlinear ill-posed operator equations in Banach spaces on the basis of finite-dimensional regularization of the Newton-Kantorovich method
Numerical methods and programming, Tome 3 (2002) no. 1, pp. 40-51

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A general approach to constructing iterative processes for nonlinear ill-posed operator equations in Banach spaces is proposed. This approach is based on the linearization of the original equation followed by the regularization with the use of the finite-dimensional Petrov-Galerkin approximation. Various aspects of practical implementation of the processes obtained are discussed.
Keywords: nonlinear equations, Banach space, iterative regularization methods, projection methods
Mots-clés : sourcewise representation. 
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     author = {M. Yu. Kokurin and O. V. Karabanova},
     title = {Iterative processes for nonlinear ill-posed operator equations in {Banach} spaces on the basis of finite-dimensional regularization of the {Newton-Kantorovich} method},
     journal = {Numerical methods and programming},
     pages = {40--51},
     publisher = {mathdoc},
     volume = {3},
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     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2002_3_1_a2/}
}
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M. Yu. Kokurin; O. V. Karabanova. Iterative processes for nonlinear ill-posed operator equations in Banach spaces on the basis of finite-dimensional regularization of the Newton-Kantorovich method. Numerical methods and programming, Tome 3 (2002) no. 1, pp. 40-51. http://geodesic.mathdoc.fr/item/VMP_2002_3_1_a2/