Geodesic
Iterative Newton-type methods with projecting for solution of nonlinear ill-posed operator equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 2, pp. 101-111

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We propose and study a class of iterative methods of the Newton type for approximate solution of nonlinear ill-posed operator equations without the regularity property. A possible a priori information concerning the unknown solution is treated by the projecting onto a closed convex subset containing the solution. The two ways of arranging of the computational process are considered. The first one requires the stopping of iterations at an appropriate step, while the second ensures obtaining of an iterative sequence which stabilizes within a small neighborhood of the solution. 
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     author = {A. B. Bakushinskii and M. Yu. Kokurin and N. A. Yusupova},
     title = {Iterative {Newton-type} methods with projecting for solution of nonlinear ill-posed operator equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     number = {2},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_2_a1/}
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A. B. Bakushinskii; M. Yu. Kokurin; N. A. Yusupova. Iterative Newton-type methods with projecting for solution of nonlinear ill-posed operator equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 2, pp. 101-111. http://geodesic.mathdoc.fr/item/SJVM_2002_5_2_a1/