The rate of convergence of the method of steepest descent in a Euclidean norm

It is proved that the error norm in the method of steepest descent decreases at the rate of a geometric progression. An estimate is given for the rate of convergence of its decrease, that is the best possible at each step of the method, for the class of ill-posed problems. The proof is based on the idea of reduction to the case of “smallest dimension” (in the given case, to two...