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AN ITERATIVE SCHEME FOR SOLVING NONLINEAR EQUATIONS WITH MONOTONE OPERATORS

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by N. S. Hoang , A. G. Ramm
Citations:11 - 6 self
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BibTeX

@MISC{Hoang_aniterative,
    author = {N. S. Hoang and A. G. Ramm},
    title = {AN ITERATIVE SCHEME FOR SOLVING NONLINEAR EQUATIONS WITH MONOTONE OPERATORS},
    year = {}
}

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Abstract

An iterative scheme for solving ill-posed 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 ill-posed 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.

Keyphrases

monotone operator    iterative scheme    discrepancy principle    dynamical system method    ill-posed nonlinear operator equation    discrete version    ill-posed operator equation    stable solution    posteriori stopping rule   

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