Dynamical Systems Method of gradient type for solving nonlinear equations with monotone operators

Dynamical Systems Method of gradient type for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Method (DSM) of gradient type for solving equation F ( u )= f where F : H → H is a monotone Fréchet differentiable operator in a Hilbert space H is studied in this paper. A discrepancy principle is proposed and the convergence to the minimal-norm solution is justif...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:BIT (Nordisk Tidskrift for Informationsbehandling) 2010-12, Vol.50 (4), p.751-780
1. Verfasser: Hoang, N. S.
Format: Artikel
Sprache:eng
Schlagworte:
Computational Mathematics and Numerical Analysis
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:A version of the Dynamical Systems Method (DSM) of gradient type for solving equation F ( u )= f where F : H → H is a monotone Fréchet differentiable operator in a Hilbert space H is studied in this paper. A discrepancy principle is proposed and the convergence to the minimal-norm solution is justified. Based on the DSM an iterative scheme is formulated and the convergence of this scheme to the minimal-norm solution is proved.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-010-0284-2