References
- Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Vol. 375, Mathematics and its applications Dordrecht: Kluwer; 1996.
- Vainikko GM, Veretennikov AY. Iteration procedures in ill-posed problems. Moscow: Nauka; 1986(in Russian).
- Tautenhahn U. On a new parameter choice rule for ill-posed inverse problems. In: Lipitakis EA, editor. HERCMA ’98: Proc. 4th Hellenic-European Conference on Computer Mathematics and its Applications. Athens: Lea Publishers; 1999. p. 118–125.
- Hämarik U. Monotonicity of error and choice of the stopping index in iterative regularization methods. In: Pedas A, editor. Differential and integral equations: theory and numerical analysis. Tartu: Estonian Mathematical Society; 1999. p. 15–30.
- Hämarik U, Raus T. On the a posteriori parameter choice in regularization methods. Proc. Estonian Acad. Sci. Phys. Math. 1999;48:133–145.
- Tautenhahn U, Hämarik U. The use of monotonicity for choosing the regularization parameter in ill-posed problems. Inverse Probl. 1999;15:1487–1505.
- Hämarik U, Tautenhahn U. On the monotone error rule for parameter choice in iterative and continuous regularization methods. BIT Numerical Math. 2001;41:1029–1038.
- Hämarik U, Tautenhahn U. On the monotone error rule for choosing the regularization parameter in ill-posed problems. In: Lavrentiev MM, Kabanikhin SI, editors. Ill-posed and non-classical problems of mathematical physics and analysis. Utrecht: VSP; 2003 p. 27–55.
- Alifanov OM, Rumyantsev SV. On the stability of iterative methods for the solution of linear ill-posed problems. Soviet Math. Dokl. 1979;20:1133–1136.
- Alifanov OM, Artyukhin EA. Rumyantsev SV. Extreme methods for solving ill-posed problems with applications to inverse heat transfer problems. New York: Begell House; 1995.
- Egger H. Y-scale regularization. SIAM J. Numer. Anal. 2008;46:419–436.
- Egger H. Regularization of inverse problems with large noise. J. Phys.: Conf. Ser. 2008; 124: 9pp.
- Morozov VA. Regularization under large noise. Comput. Math. Math. Phys. 1996;36:1175–1181.
- Eggermont PPB, LaRiccia VN, Nashed MZ. On weakly bounded noise in ill-posed problems. Inverse Prob. 2009; 25: 14 p.
- Mathé P, Tautenhahn U. Enhancing linear regularization to treat large noise. J. Inverse Ill-Posed Prob. 2011;19:859–879.
- Mathé P, Tautenhahn U. Regularization under general noise assumptions. Inverse Prob. 2011; 27:035016 (15 p).
- Vainikko GM. The discrepancy principle for a class of regularization methods. USSR Comp. Math. Math. Phys. 1982;22:1–19.
- Hämarik U, Palm R, Raus T. Use of extrapolation in regularization methods. J. Inverse Ill-Posed Prob. 2007;15:277–294.
- Hämarik U, Palm R, Raus T. Extrapolation of Tikhonov regularization method. Math. Model. Anal. 2010;15:55–68.
- Tautenhahn U. Error estimates for regularization methods in Hilbert scales. SIAM J. Numer. Anal. 1996;33:2120–2130.
- Morozov VA. On the solution of functional equations by the method of regularization. Soviet Math. Dokl. 1966;7:414–417.
- Raus T. On the discrepancy principle for solution of ill-posed problems with non-selfadjoint operators. Acta et comment. Univ. Tartuensis. 1985;715: 12–20(in Russian).
- Gfrerer H. An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Math. Comp. 1987;49:507–522.
- Tautenhahn U. On order optimal regularization under general source conditions. Proc. Est. Acad. Sci. Phys. Math 2004;53: 116–123.
- Hämarik U, Palm R, Raus T. A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level. J. Comput. Appl. Math. 2012;236:2146–2157.
- Hämarik U, Palm R, Raus T. Comparison of parameter choices in regularization algorithms in case of different information about noise level. Calcolo. 2011;48:47–59.
- Hämarik U, Kangro U, Palm R, Raus T. On parameter choice in the regularization of ill-posed problems with rough estimate of the noise level of the data. In: Numerical analysis and applied mathematics ICNAAM 2012. AIP Conference Proceedings, 1479. New York (NY): American Institute of Physics; 2012. p. 2332–2335.
- Hämarik U, Raus T. On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data. J. Inverse Ill-Posed Prob. 2006;14:251–266.
- Hämarik U, Palm R, Raus T. On minimization strategies for choice of the regularization parameter in ill-posed problems. Numer. Funct. Anal. Opt. 2009;30:924–950.
- Hämarik U, Raus T, Palm R. On the analog of the monotone error rule for parameter choice in the (iterated) Lavrentiev regularization. Comput. Meth. Appl. Math. 2008;8:237–252.
- Palm R. Numerical comparison of regularization algorithms for solving ill-posed problems. University of Tartu; 2010. Available from: http://hdl.handle.net/10062/14623.
- Hämarik U, Palm R, Raus T. A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data. J. Inverse Ill-Posed Prob. 2012;20:831–854.
- Gilyazov SF, Goldman NL. Regularization of ill-posed problems by iteration methods. Vol. 499, Mathematics and its applications. Dordrecht: Kluwer; 2000.
- Hämarik U, Raus T. On the choice of the stopping index in iteration methods for solving problems with noisy data. In: Lipitakis EA, editor. HERCMA 2001: Proceedings of the 5th Hellenic-European conference on computer mathematics and its applications, Athens, Greece, September 20–22, 2001. Athens: Lea Publishers; 2002. p. 524–529.
- Mathé P, Pereverzev SV. Geometry of linear ill-posed problems in variable Hilbert scales. Inverse Prob. 2003;19:789–803.
- Hanke M. Conjugate gradient type methods for ill-posed problems. Harlow: Longman Scientific & Technical 1995.
- Pereverzev SV, Schock E. On the adaptive selection of the parameter in the regularization of ill-posed problems. SIAM J. Numer. Anal. 2005;43:2060–2076.
- Hämarik U, Palm R. On rules for stopping the conjugate gradient type methods in ill-posed problems. Math. Model. Anal. 2007;12:61–70.
- Hämarik U, Raus T. About the balancing principle for choice of the regularization parameter. Numer. Funct. Anal. Opt. 2009;30:951–970.
- Hanke M. Accelerated Landweber iterations for the solution of ill-posed equations. Numer. Math. 1991;60:341–373.
- Raus T, Hämarik U. On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator. Adv. Comput. Math. 2012;36:221–233.
- Hämarik U, Palm R, Raus T. On the quasioptimal regularization parameter choices for solving ill-posed problems. J. Inverse Ill-Posed Prob. 2007;15:419–439.
- Hansen PC. Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms. 1994;6:1–35.
- Eldén L. The numerical solution of a non-characteristic Cauchy problem for a parabolic equation. In: Numerical Treatment of Inverse Problems in Differential and Integral Equations, Proceedings of an International Workshop, Heidelberg,1982 Boston: Birkhäuser; 1983. p. 246–268.
- Hämarik U, Avi E, Ganina A. On the solution of ill-posed problems by projection methods with a posteriori choice of the discretization level. Math. Model. Anal. 2002;7:241–252.