Additive self-similar approximants

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory, allowing for accurate extrapolation and interpolation of asymptotic series. The method is illustrated by the examples possessing the structure typical of many nonlinear problems in mathematical chemistry. Good numerical convergence is demonstrated for the cases that can be compared with exact solutions, when these are available. The method is shown to be not less and as a rule essentially more accurate than that of Padé approximants. Comparison with other approximation methods is also given.