Geodesic
A two-sided error estimate for a regularizing method based on M.M. Lavrent'ev's method
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 238-249 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an operator equation of the first kind with error in the operator and in the right-hand side of the equation. The method is a function of this operator depending on a positive parameter $\alpha$. A lower estimate of a method of solving this equation for any value of $\alpha$ is obtained. A regularizing method based on Lavrent'ev's method is constructed, and a two-sided error estimate is obtained for this method. Discrete approximations of Lavrent'ev's method are constructed. Error estimates are obtained for these approximations. The discrete approximations were further used for a perturbation of the operator in the equation.
Keywords: operator equation; regularization; error estimation; ill-posed problem. 
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V. P. Tanana; A. I. Sidikova. A two-sided error estimate for a regularizing method based on M.M. Lavrent'ev's method. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 238-249. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a24/

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