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AN ITERATIVE SCHEME FOR SOLVING NONLINEAR EQUATIONS WITH MONOTONE OPERATORS
"... An iterative scheme for solving illposed nonlinear operator equations with monotone operators is introduced and studied in this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of illposed operator equations with monotone operators is proposed and its c ..."
Abstract

Cited by 11 (6 self)
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An iterative scheme for solving illposed nonlinear operator equations with monotone operators is introduced and studied in this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of illposed operator equations with monotone operators is proposed and its convergence is proved. A discrepancy principle is proposed and justified. A priori and a posteriori stopping rules for the iterative scheme are formulated and justified.
Dynamical systems gradient method for solving illconditioned linear algebraic systems
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Dynamical Systems Method (DSM) for solving equations with monotone operators without smoothness assumptions on F'(u)
 JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
, 2010
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Comparative Studies for Different Image Restoration Methods
, 2015
"... Abstract: Image restoration refers to the problem of removal or reduction of degradation in blurred noisy images. The image degradation is usually modeled by a linear blur and an additive white noise process. The linear blur involved is always an illconditioned which makes image restoration proble ..."
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Abstract: Image restoration refers to the problem of removal or reduction of degradation in blurred noisy images. The image degradation is usually modeled by a linear blur and an additive white noise process. The linear blur involved is always an illconditioned which makes image restoration problem an illposed problem for which the solutions are unstable. Procedures adopted to stabilize the inversion of illposed problem are called regularization, so the selection of regularization parameter is very important to the effect of image restoration. In this paper, we study some numerical techniques for solving this illposed problem. Dynamical systems method (DSM), Tikhonov regularization method, Lcurve method and generalized cross validation (GCV) are presented for solving this illposed problems. Some test examples and comparative study are presented. From the numerical results it is clear that DSM showed improved restored images compared to Lcurve and GCV.
DSM of Newton type for solving operator equations F(u) = f with minimal smoothness assumptions on F
 JOURN. COMP. SCI AND MATH., 3, N1/2, (2010), 355
, 2010
"... This paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F (u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously Fréchet diffe ..."
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This paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F (u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′ (u) are imposed. The DSM for solving equation (*) is developed. Under weak assumptions global existence of the solution u(t) is proved, the existence of u(∞) is established, and the relation F(u(∞)) = f is obtained. The DSM is developed for a stable solution of equation (*) when noisy data fδ are given, ‖‖f − fδ‖‖ ≤ δ.