On Error Estimates for Regularizing Algorithm Based on Generalized Residual Method when Solving Integral Equations

Abstract

It is necessary to solve problems that don't meet conditions of a Hadamard correctness in case of mathematical simulation of many processes and the phenomena occurring in the nature and society. The main difficulty in solving such problems is that mathematical model and method must be linked to one another. Such problems are called ill-posed problems. The bases for the solution of such tasks were laid down in the works of academicians A.N. Tikhonov, M.M. Lavrentiev, corresponding member V.K. Ivanov.

Special regular methods are created for an effective solution of unstable tasks, based on changeover of the initial incorrect task by the task or sequence of tasks, incorrect in normal sense.

This article is devoted to estimation error of regularizing algorithm based on generalized residual method. The task is incorrect. We have a difficulty associated with the uncertainly of the exact solution in case of the error evaluation of solution methods of ill-posed problem. Therefore it is necessary to develop new effective methods of solution of inverse problems of solid state physics, assess their effectiveness and develop the programs for numerical solution of these tasks. The error evaluation is received for the sampled decision on the basis of the generalized residual method.