Development of non-linear transformations for improving convergence of sequences

Abstract

A method of generating non-linear transformations for increasing the rate and expanding the domain of convergence of sequences is presented. These transformations represent in a certain sense a generalization of the well-known transformations due to Shanks, and in many cases are more efficient.

The transformations would seem to have important application in computing results from formal solutions to problems in applied mathematics when these solutions are obtained in the form of series or sequences having poor convergence. An indication is also given of application to the“evaluation”of divergent formal solutions.

^†Part of a thesis submitted towards the M.Sc. degree of the Tel-Aviv University.

^†Part of a thesis submitted towards the M.Sc. degree of the Tel-Aviv University.

Notes

^†Part of a thesis submitted towards the M.Sc. degree of the Tel-Aviv University.