A posteriori accuracy estimations of solutions to ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

Tikhonov, A.N., Leonov, A.S., and Yagola, A.G., Nelineinye nekorrektnye zadachi (Nonlinear Ill-Posed Problems), Moscow: Nauka, 1995.

Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods of Solving Ill-Posed Problems), Moscow: Nauka, 1979.

Ivanov, V.K., Vasin, V.V., and Tanana, V.P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya (Theory of Linear and Ill-Posed Problems and Its Applications), Moscow: Nauka, 1978.

Morozov, V.A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach (RegularMethods of Solving Ill-Posed Problems), Moscow: Nauka, 1987.

Leonov, A.S., Reshenie nekorrektno postavlennykh obratnykh zadach. Ocherk teorii, prakticheskie algoritmy i demonstratsii vMATLAB (Solving Ill-Posed Inverse Problems.Review of the Theory, Practical Algorithms, and Demonstrations in the MATLAB Environment), Moscow: URSS, 2009.

Tanana, V.P., Metody resheniya operatornykh uravnenii (Methods of Solving Operator Equations), Moscow: Nauka, 1981.

Tanana, V.P., Rekant, M.A., and Yanchenko, S.I., Optimizatsiya metodov resheniya operatornykh uravnenii (Optimization of Methods of Solving Operator Equations), Sverdlovsk: Ural. Univ., 1987.

Vainikko, G.M., Metody resheniya lineinykh nekorrektno postavlennykh zadach v gil’bertovykh prostranstvakh (Methods of Solving Linear Ill-Posed Problems in Hilbert Spaces), Tartu: Tartu Univ., 1982.

Bakushinskii, A.B. and Goncharskii, A.V., Iterativnye metody resheniya nekorrektnykh zadach (Iterative Methods of Solving Ill-Posed Problems), Moscow: Nauka, 1989.

Engl, H.W., Hanke, M., and Neubauer, A., Regularization of Inverse Problems, Dordrecht: Kluwer, 1996.

Dombrovskaya, I.N. and Ivanov, V.K., On the Theory of Linear Equations in Abstract Spaces, Sib.Mat. Zh., 1965, vol. 6, no. 3, pp. 499–508.

Gaponenko, Yu.L. and Vinokurov, V.A., A Posteriori Estimations of Solutions of Ill-Posed Inverse Problems, 1982, Dokl. Akad. Nauk SSSR, vol. 263, no. 2, pp. 277–280.

Yagola, A.G., Nikolaeva, N.N., and Titarenko, V.N., Estimation of the Error of the Solution of the Abel Equation on Sets of Monotonic and Convex Functions, Sib. Zh. Vych. Mat., 2003, vol. 6, no. 2, pp. 171–180.

Titarenko, V.N. and Yagola, A.G., The Problems of Linear and Quadratic Programming for Ill-Posed Problems on Some Compact Sets, 2003, J. Inv. Ill-Posed Problems, vol. 11, no. 3, pp. 311–328.

Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach (Theory of Extreme Problems), Moscow: Nauka, 1974.

Vasil’ev, F.P., Metody optimizatsii (Optimization Methods), Moscow: Faktorial Press, 2002.

Leonov, A.S., On A PosterioriAccuracy Estimations of Solutions of Linear Ill-Posed Problems and Extraoptimal Regularizing Algorithms, Vych. Metody Program., 2010, vol. 11, no. 1, pp. 14–24.

Leonov, A.S., Numerical Piecewise-Uniform Regularization for Two-Dimensional Ill-Posed Problems, Inv. Problems, 1999, vol. 15, pp. 1165–1176.

Tikhonov, A.N., Goncharskii, A.V., Stepanov, V.V., and Yagola, A.G., Chislennye metody resheniya nekorrektnykh zadach (NumericalMethods of Solving Ill-Posed Problems), Moscow: Nauka, 1990.

Leonov, A.S., On Elimination of Saturation of Accuracy of Regularizing Algorithms, Sib. Zh. Vych. Mat., 2008, vol. 11, no. 2, pp. 167–186.

Chavent, G., Non Linear Least Squares for Inverse Problems. Scientific Computation, Springer, 2009.