References
- K.I. Babenko. Approximation of periodic functions of many variables by trigonometric polynomials. Dokl. Acad. Nauk SSSR, 132(2):247–250, 1960.
- F. Bauer and T. Hohage. A Lepsij-type stopping rule for regularized Newton methods. Inverse Probl., 21(6):1975–1991, 2005. https://doi.org/10.1088/0266-5611/21/6/011.
- U. Hämarik and T. Raus. About the balancing principal for choice of the regularization parameter. Num. Func. Anal. and Optim., 30(9–10):951–970, 2009. https://doi.org/10.1080/01630560903393139.
- T. Hohage. Regularization of exponentially ill-posed problems. Numer. Funct. Anal. Optim., 21(3–4):439–464, 2000. https://doi.org/10.1080/01630560008816965.
- V.K. Ivanov. The approximate solution of operator equations of the first kind. Zh. Vychisl. Mat. Mat. Fiz., 6(6):197–205, 1966. https://doi.org/10.1016/0041-5553(66)90171-6. (in Russian)
- O. Lepskii. A problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl., 36:454–466, 1990.
- Sh. Lu and S.V. Pereverzev. Regularization Theory for Ill-posed Problems. Selected Topics. Inverse and Ill-posed Problems Series, 58. De Gruyter, Berlin, 2013. https://doi.org/10.1515/9783110286496.
- B.A. Mair. Tikhonov regularization for finitely and infinitely smoothing operators. SIAM J. Math. Anal., 25(1):135–147, 1994. https://doi.org/10.1137/S0036141092238060.
- P. Mathe and S.V. Pereverzev. Discretization strategy for ill-posed problems in variable Hilbert scales. Inverse Problems, 19(6):1263–1277, 2003. https://doi.org/10.1088/0266-5611/19/6/003.
- P. Mathe and S.V. Pereverzev. Complexity of linear ill-posed problems in Hilbert space. J. Complexity. Special Issue, pp. 50–67, 2016.
- V.A. Morozov. Regularization of incorrectly posed problems and the choice of regularization parameter. Zh. Vychisl. Mat. Mat. Fiz., 6(1):242–251, 1966. https://doi.org/10.1016/0041-5553(66)90046-2.
- V.A. Morozov. Choice of parameter in solving functional equations by the method of regularization. Dokl. Akad. Nauk SSSR, 175(1):170–175, 1967.
- S. Pereverzev and E. Schock. On the adaptive selection of the parameter in regularization of ill-posed problems. SIAM J. Numer. Anal., 43(5):2060–2076, 2005. https://doi.org/10.1137/S0036142903433819.
- S.V. Pereverzev. On the complexity of the problem of finding the solutions of Fredholm equations of the second kind with smooth kernels. I. Ukrain. Mat. Zh., 40(1):71–76, 1988. https://doi.org/10.1007/bf01056451.
- S.V. Pereverzev. On the complexity of the problem of finding the solutions of Fredholm equations of the second kind with smooth kernels. II. Ukrain. Mat. Zh., 41(2):169–173, 1989. https://doi.org/10.1007/BF01060382.
- S.V. Pereverzev. Hyperbolic cross and the complexity of the approximate solution of Fredholm integral equations of the second kind with differentiable kernels. Sibirsk. Mat. Zh., 32(1):85–92, 1991. https://doi.org/10.1007/bf00970164.
- S.V. Pereverzev. Optimization of projection methods for solving ill-posed problems. Computing, 55(2):113–124, 1995. https://doi.org/10.1007/BF02238096.
- S.V. Pereverzev and C. Scharipov. Information complexity of equations of second kind with compact operators in Hilbert space. J.Complexity, 8(2):176–202, 1992. https://doi.org/10.1016/0885-064X(92)90014-3.
- S.V. Pereverzev and S.G. Solodky. The minimal radius of Galerkin information for the Fredholm problems of first kind. J. Complexity, 12(4):401–415, 1996. https://doi.org/10.1006/jcom.1996.0025.
- R. Plato and G.M. Vainikko. On the regularization of projection methods for solving ill-posed problems. Numer. Math., 57(1):63–79, 1990. https://doi.org/10.1007/BF01386397.
- E. Schock and S.V. Pereverzev. Morozov’s discrepancy principle for Tikhonov regularization of severely ill-posed problems in finite-dimensional subspaces. Numer. Funct. Anal. Optim., 21(7–8):901–916, 2000.
- S.G. Solodky. Optimal approximation for solving linear ill-posed problems. J.Complexity, 15(4):123–132, 1999.
- S.G. Solodky. Optimization of the projection methods for solving linear ill-posed problems. Zh. Vychisl. Mat. Mat. Fiz., 39(2):195–203, 1999.
- S.G. Solodky and G.L. Myleiko. About regularization of severely ill-posed problems by standard Tikhonov’s method with the balancing principle. Math. model. anal., 19(2):199–215, 2014. https://doi.org/10.3846/13926292.2014.909898.
- S.G. Solodky and G.L. Myleiko. The minimal radius of Galerkin information for severely ill-posed problems. Journal of Inverse and Ill-Posed Problems, 22(5):739–757, 2014. https://doi.org/10.1515/jip-2013-0035.
- S.G. Solodky and G.L. Myleiko. On optimization of projection methods for solving some classes of severely ill-posed problems. J. Appl. Anal., 95(4):826–841, 2016. https://doi.org/10.1080/00036811.2015.1036748.
- S.G. Solodky and E.V. Semenova. On the optimal order of accuracy of an approximate solution to the Symm’s integral equation. Zh. Vychisl. Mat. Mat. Fiz., 52(3):472–488, 2012.
- S.G. Solodky and E.V. Semenova. About minimal informational efforts by solving exponantially ill-posed problems. Journal of Num. and Appl. Math., 2:90–100, 2015.
- U. Tautenhahn. Optimality for ill-posed problems under general source condition. Numer. Funct. Anal. Optim., 19(3–4):377–398, 1998. https://doi.org/10.1080/01630569808816834.
- J.F. Traub, G. Wasilkowski and H. Wozniakowski. A General Theory of Optimal Algorithms. Academic Press.–New York., 1980.
- J.F. Traub, G. Wasilkowski and H. Wozniakowski. Information-Based Complexity. Boston: Academic Press, 1988.
- G.M. Vainikko and A.Yu. Veretennikov. Iteration Procedures in Ill-posed Problems. Nauka, Moscow, 1986. ( in Russian)