ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65J15, 65J20, 47H17
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. In this paper we derive convergence rates results for Landweber iteration in Hilbert scales in terms of the iteration index $k$ for exact data and in terms of the noise level $\delta$ for perturbed data. These results improve the one obtained recently for Landweber iteration for nonlinear ill-posed problems in Hilbert spaces. For numerical computations we have to approximate the nonlinear operator and the infinite-dimensional spaces by finite-dimensional ones. We also give a convergence analysis for this finite-dimensional approximation. The conditions needed to obtain the rates are illustrated for a nonlinear Hammerstein integral equation. Numerical results are presented confirming the theoretical ones.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050487
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