Optimization of Methods for Solving Inverse Problems

We consider an operator equation of the first kind with the 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 for solving this equation for any value of $\alpha$ is obtained. A regularizing method based on the Lavrent'ev's method is constructed, and a two-sided error estimate is obtained for this method. The discrete approximations of the Lavrent'ev's method are constructed. Error estimates are obtained for this approximations. The discrete approximations were further used for a perturbation of the operator in the equation.