On numerical realization of quasioptimal parameter choices in (Iterated) Tikhonov and Lavrentiev regularization

Mathematical Modelling and Analysis

Volumn 14, Issue 1, 2009, Pages 99-108

  Raus, T ^a   Hamarik U ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

(iterated) Lavrentiev method; (iterated) Tikhonov method; Ill posed problem; Numerical schemes; Parameter choice; Quasioptimal rules; Regularization

Indexed keywords

NUMERICAL METHODS;

(ITERATED) LAVRENTIEV METHOD; ILL POSED PROBLEM; NUMERICAL SCHEME; PARAMETER CHOICE; QUASI-OPTIMAL; REGULARIZATION; TIKHONOV METHOD;

PARAMETERIZATION;

EID: 73449138181     PISSN: 13926292     EISSN: 16483510     Source Type: Journal    
DOI: 10.3846/1392-6292.2009.14.99-108     Document Type: Article

References (17)

1. H. Gfrerer. An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Math. Comp., 49(180):507-522, 1987.
2. U. Hämarik, R. Palm and T. Raus. Use of extrapolation in regulaxization methods. Journal of Inverse and Ill-Posed Problems, 15(3):277-294, 2007.
3. U. Hämarik, T. Raus and R. Palm. On the analog of the monotone error rule for parameter choice in the (iterated) Lavrentiev regularization. Computational Methods in Applied Mathematics, 8(3):237-252, 2008.
4. T. Hohage. Regularization of exponentially ill-posed problems. Numerical Functional Analysis and Optimization, 21(3):439-464, 2000.
5. P. Mathé and S. V. Pereverzev. Geometry of linear ill-posed problems in variable Hubert scales. Inverse Problems, 19(3):789-803, 2003.
6. V. A. Morozov. On the solution of functional equations by the method of regularization. Soviet Math. Dokl., 7:414-417, 1966.
7. M. T. Nair, S. V. Pereverzev and U. Tautenhahn. Regularization in Hilbert scales under general smoothing conditions. Inverse Problems, 21(6):1851-1869, 2005.
8. [8] S. V. Pereverzev and E. Schock. On the adaptive selection of the parameter in the regularization of ill-posed problems. SIAM J. Numerical Analysis, 43(5):2060-2076, 2005. (Pubitemid 44598672)
9. T. Raus. Residue principle for ill-posed problems. Acta et Comment Univ. Tartuensis, 672:16-26, 1984. (in Russian)
10. T. Raus. On the discrepancy principle for solution of ill-posed problems with nonselfadjoint operators. Acta et Comment. Univ. Tartuensis, 715:12-20, 1985. (in Russian)
11. T. Raus. An a posteriori choice of the regularization parameter in case of approximately given error bound of data. Acta et Comment. Univ. Tartuensis, 913:73-87, 1990.
12. T. Raus. About regularization parameter choice in case of approximately given error bounds of data. Acta et Comment. Univ. Tartuensis, 937:77-89, 1992.
13. [13] T. Raus and U. Hämarik. On the quasioptimal regularization parameter choices for solving ill-posed problems. Journal of Inverse and Ill-Posed Problems, 15(4):419-439, 2007. (Pubitemid 47213847)
14. [14] U. Tautenhahn. Optimality for ill-posed problems under general source conditions. Numer. Funct. Anal Optim., 19(3-4):377-398, 1998. (Pubitemid 128508292)
15. U. Tautenhahn and U. Hämarik. The use of monotonicity for choosing the regularization parameter in ill-posed problems. Inverse Problems, 15(6):1487-1505, 1999.
16. G. Vainikko and A. Veretennikov. Iteration Procedures in Ill-Posed Problems. Nauka, Moscow, 1986. (in Russian)
17. G. M. Vainikko. The principle of the residual for a class of regularization methods. USSR Comput. Math. Math. Phys., 22(3):1-19, 1982.