Вычислительные методы и приложения

On optimal methods for solving ill-posed problems

V. A. Morozov

Lomonosov Moscow State University, Research Computing Center

Abstract: The problem of constructing an optimal algorithm for finding the operator values on the solution of an operator equation with exact and approximate initial data is considered. The structure of such an algorithm is discussed. The order-of-magnitude optimality of several well-known methods for solving ill-posed problems is proved (in particular, the regularization method with regularization parameter choice on the basis of the residual principle, the residual operator method, and the method of quasisolutions are analyzed for various ways of apriori information specification). Two examples are examined. The work was supported by the Russian Foundation for Basic Research (04-01-00026).

Keywords: ill-posed problems, optimal algorithms, regularization method, residual principle, regularization parameter.

UDC: 519.6