An iterative scheme for solving nonlinear equations with monotone operators

An iterative scheme for solving nonlinear equations with monotone operators

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 c...

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Veröffentlicht in:BIT (Nordisk Tidskrift for Informationsbehandling) 2008-12, Vol.48 (4), p.725-741
Hauptverfasser: Hoang, N.S., Ramm, A.G.
Format: Artikel
Sprache:eng
Schlagworte:
Computational Mathematics and Numerical Analysis
Exact sciences and technology
Finite differences and functional equations
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Operator theory
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Zusammenfassung: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.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-008-0199-3