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An iterative stabilization method for the evaluation of unbounded operators

Author: C. W. Groetsch
Journal: Proc. Amer. Math. Soc. 134 (2006), 1173-1181
MSC (2000): Primary 65J20, 47A52; Secondary 47A58
Published electronically: July 20, 2005
MathSciNet review: 2196054
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Abstract: We investigate a stable iterative approximate evaluation method for closed unbounded operators such as those that occur frequently in inverse problems. Convergence theorems, as well as order of approximation results, are proved for both a priori and a posteriori schemes for choosing the stopping index of the iteration.

References [Enhancements On Off] (What's this?)

  • 1. C.W. Groetsch, Generalized Inverses of Linear Operators: Representation and Approximation, Dekker, New York, 1977. MR 0458859 (56:17059)
  • 2. C.W. Groetsch, Spectral methods for linear inverse problems involving unbounded operators, J. Approx. Theory 70 (1992), 16-28. MR 1168372 (93g:47011)
  • 3. C.W. Groetsch, Inverse Problems in the Mathematical Sciences, Vieweg, Braunschweig, 1993. MR 1247696 (94m:00008)
  • 4. C.W. Groetsch and O. Scherzer, Optimal order of convergence for stable evaluation of differential operators, Electron. J. Differential Equations 4 (1993), 1-10. MR 1241489 (94m:47021)
  • 5. M. Hanke and C.W. Groetsch, Nonstationary iterated Tikhonov regularization, J. Optimization Theory Appl. 98(1998), 37-53. MR 1633299 (99e:65100)
  • 6. L.J. Lardy, A series representation of the generalized inverse of a closed linear operator, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), 152-157. MR 0473881 (57:13540)
  • 7. V.A. Morozov, Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, 1984. MR 0766231 (86d:65005)
  • 8. F. Riesz and B. Sz.-Nagy, Functional Analysis, Ungar, New York, 1955. MR 0071727 (17:175i)

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Additional Information

C. W. Groetsch
Affiliation: Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221-0025

Keywords: Inverse problem, ill-posed problem, unbounded operator, stabilized evaluation
Received by editor(s): November 22, 2003
Received by editor(s) in revised form: October 25, 2004
Published electronically: July 20, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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