A posteriori error estimates in linear ill-posed problems

Abstract A posteriori error estimates for approximate solutions of linear ill-posed inverse problems are under investigation. A brief overview of existing approaches to this problem is given. Special variational a posteriori error estimates are studied for various classes of function spaces. Obtaining all such estimates reduces to solving a certain canonical problem. For the canonical problem, a solution algorithm is given in various forms. This algorithm is several times faster than previously proposed ones. The estimates and algorithm are suitable for various Hilbert and Banach spaces. The obtaining of such estimates is illustrated using the example of a two-dimensional model inverse problem of heat conduction.