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 Num. Meth. Prog., 2015, Volume 16, Issue 1, Pages 1–9 (Mi vmp513)

An error estimate of a regularizing algorithm based of the generalized residual principle when solving integral equations

V. P. Tanana, A. I. Sidikova

South Ural State University, Chelyabinsk

Abstract: 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.

Full text: PDF file (185 kB)
UDC: 517.948

Citation: V. P. Tanana, A. I. Sidikova, “An error estimate of a regularizing algorithm based of the generalized residual principle when solving integral equations”, Num. Meth. Prog., 16:1 (2015), 1–9

Citation in format AMSBIB
\Bibitem{TanSid15} \by V.~P.~Tanana, A.~I.~Sidikova \paper An error estimate of a regularizing algorithm based of the generalized residual principle when solving integral equations \jour Num. Meth. Prog. \yr 2015 \vol 16 \issue 1 \pages 1--9 \mathnet{http://mi.mathnet.ru/vmp513}