"An error estimate of a regularizing algorithm based of the generalized residual principle when solving integral equations"
Tanana V.P. and Sidikova A.I.

A regularizing algorithm for the approximate solution of integral equations of the first kind is studied. This algorithm involves a finite-dimensional approximation of the original problem. An error estimate is proposed. In order to obtain this estimate, the equivalence of the generalized residual method and the generalized residual principle is proved. This result can be used to estimate the finite-dimensional approximations of regularized solutions.

Keywords: regularization, generalized residual method, modulus of continuity, error estimates, ill-posed problems, integral equations, operator equations, finite-dimensional approximations.

  • Tanana V.P. – South Ural State University, Faculty of Computational Mathematics and Informatics; prospekt Lenina 76, Chelyabinsk, 454080, Russia; Dr. Sci., Professor, Head of Department, e-mail: tvpa@susu.ac.ru
  • Sidikova A.I. – South Ural State University, Faculty of Computational Mathematics and Informatics; prospekt Lenina 76, Chelyabinsk, 454080, Russia; Ph.D., Associate Professor, e-mail: 7413604@mail.ru