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Nonlinear Tikhonov regularization in Hilbert scales for inverse boundary value problems with random noise
On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
1. | Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz, Austria |
2. | Industrial Mathematics Institute, Johannes Kepler University Linz A-4040 Linz, Austria |
References:
[1] |
M. A. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Am. Math. Soc., 320 (1990), 727-735.
doi: 10.2307/2001699. |
[2] |
A. B. Bakushinskii, Remarks on the choice of regularization parameter from quasioptimality and relation tests, (Russian) Zh. Vychisl. Mat. i Mat. Fiz., 24 (1984), 1258-1259. |
[3] |
F. Bauer and S. Kindermann, The quasi-optimality criterion for classical inverse problems, Inverse Problems, 24 (2008). |
[4] |
H. W. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems,'' Mathematics and its Applications, 375. Kluwer Academic Publishers Group, Dordrecht, 1996. |
[5] |
M. Hanke and P. C. Hansen, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), 253-315. |
[6] |
A. S. Leonov, On the choice of regularization parameters by means of the quasi-optimality and ratio criteria, Soviet Math. Dokl., 19 (1978), 537-540. |
[7] |
A. S. Leonov, On the accuracy of Tikhonov regularizing algorithms and quasioptimal selection of a regularization parameter, Soviet Math. Dokl., 44 (1992), 711-716. |
[8] |
A. Neubauer, On converse and saturation results for regularization methods, in "Beiträge zur Angewandten Analysis und Informatik,'' Shaker, Aachen, (1994), 262-270. |
[9] |
A. Neubauer, On converse and saturation results for Tikhonov regularization of linear ill-posed problems, SIAM J. Numer. Anal., 34 (1997), 517-527.
doi: 10.1137/S0036142993253928. |
[10] |
A. N. Tikhonov and V. Arsenin, "Solutions of Ill-Posed Problems,'' Wiley, New York, 1977. |
[11] |
A. N. Tikhonov, V. B. Glasko and Y. Kriksin, On the question of quasioptimal choice of a regularized approximation, Soviet Math. Dokl., 20 (1979), 1036-1040. |
show all references
References:
[1] |
M. A. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Am. Math. Soc., 320 (1990), 727-735.
doi: 10.2307/2001699. |
[2] |
A. B. Bakushinskii, Remarks on the choice of regularization parameter from quasioptimality and relation tests, (Russian) Zh. Vychisl. Mat. i Mat. Fiz., 24 (1984), 1258-1259. |
[3] |
F. Bauer and S. Kindermann, The quasi-optimality criterion for classical inverse problems, Inverse Problems, 24 (2008). |
[4] |
H. W. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems,'' Mathematics and its Applications, 375. Kluwer Academic Publishers Group, Dordrecht, 1996. |
[5] |
M. Hanke and P. C. Hansen, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), 253-315. |
[6] |
A. S. Leonov, On the choice of regularization parameters by means of the quasi-optimality and ratio criteria, Soviet Math. Dokl., 19 (1978), 537-540. |
[7] |
A. S. Leonov, On the accuracy of Tikhonov regularizing algorithms and quasioptimal selection of a regularization parameter, Soviet Math. Dokl., 44 (1992), 711-716. |
[8] |
A. Neubauer, On converse and saturation results for regularization methods, in "Beiträge zur Angewandten Analysis und Informatik,'' Shaker, Aachen, (1994), 262-270. |
[9] |
A. Neubauer, On converse and saturation results for Tikhonov regularization of linear ill-posed problems, SIAM J. Numer. Anal., 34 (1997), 517-527.
doi: 10.1137/S0036142993253928. |
[10] |
A. N. Tikhonov and V. Arsenin, "Solutions of Ill-Posed Problems,'' Wiley, New York, 1977. |
[11] |
A. N. Tikhonov, V. B. Glasko and Y. Kriksin, On the question of quasioptimal choice of a regularized approximation, Soviet Math. Dokl., 20 (1979), 1036-1040. |
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