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Dynamical systems method for solving nonlinear equations with monotone operators
Author(s):
N.
S.
Hoang;
A.
G.
Ramm.
Journal:
Math. Comp.
79
(2010),
239-258.
MSC (2000):
Primary 65R30;
Secondary 47J05, 47J06, 47J35
Posted:
April 2, 2009
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Additional information
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:
10.1090/S0025-5718-09-02260-1
PII:
S 0025-5718(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
Posted:
April 2, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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