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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

Dynamical systems method for solving nonlinear equations with monotone operators


Authors: N. S. Hoang and A. G. Ramm
Journal: Math. Comp. 79 (2010), 239-258
MSC (2000): Primary 65R30; Secondary 47J05, 47J06, 47J35
Published electronically: April 2, 2009
MathSciNet review: 2552225
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Abstract: A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type principle is proposed and justified mathematically. The results of two numerical experiments are presented. They show that the proposed version of DSM is numerically efficient. The numerical experiments consist of solving nonlinear integral equations.


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Additional Information

N. S. Hoang
Affiliation: Mathematics Department, Kansas State University, Manhattan, Kansas 66506-2602
Email: nguyenhs@math.ksu.edu

A. G. Ramm
Affiliation: Mathematics Department, Kansas State University, Manhattan, Kansas 66506-2602
Email: ramm@math.ksu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-09-02260-1
Keywords: Dynamical systems method (DSM), nonlinear operator equations, monotone operators, discrepancy principle
Received by editor(s): April 3, 2008
Received by editor(s) in revised form: January 17, 2009
Published electronically: April 2, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.