ИСТИНА

In order to calculate a priori or a posteriori error estimates for solutions of an ill-posed operator equation with an injective operator we need to describe a set of approximate solutions that contains an exact solution. After that we have to calculate a diameter of this set or maximal distance from a fixed approximate solution to any element of this set. I will describe three approaches for constructing error estimates and also their practical applications in solving the inverse elastography problem and the inverse problem of microtomography. This work was supported by the RFBR grant 17-01-00159 and the RFBR-NSCF grant 19-51-53005. References: [1] A Yagola, V Titarenko, Using a priori information about a solution of an ill-posed problem for constructing regularizing algorithms and their applications, Inverse Problems in Science and Engineering, Vol. 15, No. 1, 3-17, 2007. [2] A S Leonov, A N Sharov and A G Yagola, Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate, Journal of Inverse and Ill-Posed Problems, Vol. 26, issue 4, 493-500, 2018. [3] A S Leonov, Y Wang and A G Yagola, Piecewise uniform regularization for the inverse problem of microtomography with a-posteriori error estimate, Inverse Problems in Science and Engineering, published online, 2018, DOI: 10.1080/17415977.2018.1561676