Nonlinear Sequence Transformations: Computational Tools for the Acceleration of Convergence and the Summation of Divergent Series [article]

Ernst Joachim Weniger (Institute for Physical and Theoretical Chemistry, University of Regensburg, Regensburg, Germany)
2001 arXiv   pre-print
Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by converting a slowly converging or diverging input sequence {s_n }_n=0^∞ into another sequence {s^'_n }_n=0^∞ with hopefully better numerical properties. Padé approximants, which convert the partial sums of a power series to a doubly indexed sequence of rational
more » ... tions, are the best known sequence transformations, but the emphasis of the review will be on alternative sequence transformations which for some problems provide better results than Padé approximants.
arXiv:math/0107080v1 fatcat:rsge4qizzvea7etakrbqq6kqje