Numerical method for solving the inverse scattering problem, based on the asymptotic regularization

The numerical method for the inverse problem of quantum scattering theory is suggested. It is based on the two asymptotic regularizations: the first one uses the asymptotic behaviours of the phase shift and of the module of the Jost function for high energies, and the second one – the asymptotics by step of the reciprocals to “almost” Toeplitz and Hankel matrices. The last one permits to avoid the unstable procedure of the numerical differentiation.