References
- G. Bruckner and S.V. Pereverzev. Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems. Inverse Problems, 19(1):147–156, 2003. http://dx.doi.org/10.1088/0266-5611/19/1/308.
- H.W. Engl. On the convergence of regularization methods for ill-posed linear operator equations. In G. Hämmerlin and K.-H. Hoffmann (Eds.), Improperly Posed Problems and Their Numerical Treatment, pp. 81–95. Birkhäuser, 1983.
- H.W. Engl, M. Hanke and A. Neubauer. Regularization of Inverse Problems. Kluwer, Dordrecht, 1996.
- V.M. Fridman. New methods of solving a linear operator equation. Dokl. Akad. Nauk SSSR, 128:482–484, 1959.
- U. Hämarik. Projection methods for the regularization of linear ill-posed problems. Proc. Comput. Center Tartu Univ., 50:69–90, 1983.
- U. Hämarik. Monotonicity of error and choice of the stopping index in iterative regularization methods. In A. Pedas (Ed.), Differential and Integral Equations: Theory and Numerical Analysis, pp. 15–30. Estonian Math. Society, Tartu, 1999.
- U. Hämarik, E. Avi and A. Ganina. On the solution of ill-posed problems by projection methods with a posteriori choice of the discretization level. Math. Model. Anal., 7(2):241–252, 2002. http://dx.doi.org/10.1080/13926292.2002.9637196.
- U. Hämarik, U. Kangro, R. Palm, T. Raus and U. Tautenhahn. Monotonicity of error of regularized solution and its use for parameter choice. Inverse Probl. Sci. Eng., 22(1):10–30, 2014. http://dx.doi.org/10.1080/17415977.2013.827185.
- U. Hämarik and U. Tautenhahn. On the monotone error rule for parameter choice in iterative and continuous regularization methods. BIT, 41(5):1029–1038, 2001. http://dx.doi.org/10.1023/A:1021945429767.
- H. Harbrecht, S. Pereverzev and R. Schneider. Self–regularization by projection for noisy pseudodifferential equations of negative order. Numer. Math., 95(1):123–143, 2003. http://dx.doi.org/10.1007/s00211-002-0417-x.
- B. Hofmann, P. Mathé and S.V. Pereverzev. Regularization by projection: approximation theoretic aspects and distance functions. J. Inverse Ill-Posed Probl., 15(5):527–545, 2007. http://dx.doi.org/10.1515/jiip.2007.029.
- V.K. Ivanov, V.V. Vasin and V.P. Tanana. The Theory of Linear Ill-Posed Problems and its Applications. Nauka, Moscow, 1978. ( in Russian)
- B. Kaltenbacher. Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems. Inverse Problems, 16(5):1523–1539, 2000. http://dx.doi.org/10.1088/0266-5611/16/5/322.
- B. Kaltenbacher. On the regularizing properties of a full multigrid method for ill-posed problems. Inverse Problems, 17(4):767–788, 2001. http://dx.doi.org/10.1088/0266-5611/17/4/313.
- B. Kaltenbacher. V-cycle convergence of some multigrid methods for ill-posed problems. Math. Comp., 72(244):1711–1730, 2003. http://dx.doi.org/10.1090/S0025-5718-03-01533-3.
- B. Kaltenbacher and J. Offtermatt. A convergence analysis of regularization by discretization in preimage space. Math. Comp., 81(280):2049–2069, 2012. http://dx.doi.org/10.1090/S0025-5718-2012-02596-8.
- P. Mathé and S.V. Pereverzev. Optimal discretization of inverse problems in Hilbert scales. regularization and self-regularization of projection methods. SIAM J. Numer. Anal., 38(6):1999–2021, 2001. http://dx.doi.org/10.1137/S003614299936175X.
- P. Mathé and N. Schöne. Regularization by projection in variable Hilbert scales. Appl. Anal., 87(2):201–219, 2008. http://dx.doi.org/10.1080/00036810701858185.
- W.V. Petryshyn. Direct and iterative methods for the solution of linear operator equations in Hilbert space. Trans. Amer. Math. Soc., 105(1):136–175, 1962. http://dx.doi.org/10.1090/S0002-9947-1962-0145651-8.
- D.L. Phillips. A technique for the numerical solution of certain integral equations of the first kind. J. Assoc. Comput. Mach., 9:84–97, 1962. http://dx.doi.org/10.1145/321105.321114.
- G.R. Richter. Numerical solution of integral equations of the first kind with nonsmooth kernels. SIAM J. Numer. Anal., 15(3):511–522, 1978. http://dx.doi.org/10.1137/0715033.
- T.I. Seidman. Convergent approximation methods for ill-posed problems, Part I: general theory. Control Cybernet., 10:31–49, 1981.
- G.M. Vainikko and U. Hämarik. Projection methods and self-regularization in ill-posed problems. Soviet Math., 29(10):1–20, 1985.
- G.M. Vainikko and A.Yu. Veretennikov. Iteration Procedures in Ill-Posed Problems. Nauka, Moscow, 1986. ( in Russian)