Numerical analysis of convergent perturbation theory in quantum field theory

Results of numerical analysis of convergency for a new series of perturbation theory are presented. Two examples are considered: anharmonic oscillator in quantum mechanics and the renormalization group $\beta$-function in field theory. It is shown that in the former case the series converges to an exact value in the wide region of the expansion parameter. This region can be enlarged by using the Padé approximation. In the field theory case the results have the stronger dependence on the expansion parameter. An algorithm of choosing this parameter in such a way as to obtain stable results is discussed.