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An Approach to Solving Ill-posed Problems
The solving of integral equations of the first kind whose input is known only approximately is considered. In this classical ill-posed problem, the
standard regularization techniques are not efficient at insufficient accuracy of an input. New techniques are presented and tested with exactly solvable examples. The problem proves to turn to a well-posed one in a certain sense. Inversions of the Lorentz, Stieltjes, and Laplace integral transforms at approximate inputs are performed, and very satisfactory results are obtained. The present method may be useful, in particular, for the calculation of few- or many-body many-channel reactions in the framework of the integral transform approach.