Methods of identifying a parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities
Tatiana Vladimirovna Antonova
Institute of Mathematics and Mechanics Ural Branch of Russian Academy of Scienes, 16 S. Kovalevskaya str., Ekaterinburg, Russia, 620990
Keywords: ill-posed problems, localization of singularities, equation of the first kind, parameter identification
Abstract
In this paper, we propose a regular iterative method of identifying a numerical parameter in the kernel of the integral equation of the first kind of the convolution type. It is shown that an unambiguous identification of the parameter is possible when an exact solution has discontinuities of the first kind. The convergence theorem is proved, and an example of the equation with a parameter, for which the method constructed is applicable, is given.
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