Numerical implementation of special regularizing algorithms for solving a class of ill-posed problems with sourcewise represented solutions

An important class of ill-posed problems, namely, inverse problems of continuation for the values of an abstract function, is under consideration. The class is associated with certain semigroups of operators. A priori, the problems of this class have sourcewise represented solutions with known powers. For solving these problems we apply special Tikhonov's regularizing algorithms of the generalized residual principle. The approximate solutions obtained by the use of the algorithms and modifications proposed are of optimal order of accuracy without regard to the positive sourcewise representation power. The algorithm is numerically implemented in an efficient way. An example of application of the algorithm is given.