Numerical algorithms for optimal methods of solving linear inverse problems: application of optimal recovery

The report is devoted to application of the theory of optimal recovery to solve linear inverse problems with a convex balanced set of a priori constraints. Last achievements are in use. Here is described a class of conditionally well-posed linear inverse problems for which an optimal solution method is managed to be constructed. Also, here is described a class of ill-posed linear inverse problems for which an optimal regularizing algorithm is managed to be constructed.