Self-similarly corrected Padé approximants for the indeterminate problem
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia
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Accepted: 28 August 2016
Published online: 27 September 2016
A method is suggested for treating the well-known deficiency in the use of Padé approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of self-similarly corrected Padé approximants, making it possible to essentially increase the class of functions treated by these approximants. The method works well even in those cases where the standard Padé approximants are not applicable, resulting in divergent sequences. Numerical convergence of our method is demonstrated by several physical examples.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016