ISSN:
1572-9265
Keywords:
ill-posed problems
;
first kind integral equations
;
conjugate gradient-type methods
;
minimal error method
;
regularization schemes
;
discrepancy principle
;
parameter estimation problems
;
65J20
;
65R30
;
45E99
;
65N38
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We consider an ill-posed problem Ta = f* in Hilbert spaces and suppose that the linear bounded operator T is approximately available, with a known estimate for the operator perturbation at the solution. As a numerical scheme the CGNR-method is considered, that is, the classical method of conjugate gradients by Hestenes and Stiefel applied to the associated normal equations. Two a posteriori stopping rules are introduced, and convergence results are provided for the corresponding approximations, respectively. As a specific application, a parameter estimation problem is considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019139414435
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