Journal ArticleDOI
Development of non-linear transformations for improving convergence of sequences
TLDR
A method of generating non-linear transformations for increasing the rate and expanding the domain of convergence of sequences is presented, which represent in a certain sense a generalization of the well-known transformations due to Shanks and are more efficient.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.read more
Citations
More filters
Journal ArticleDOI
HULLAC, an integrated computer package for atomic processes in plasmas
TL;DR: H ULLAC as mentioned in this paper, an integrated code for calculating atomic structure and cross sections for collisional and radiative atomic processes, is based on relativistic quantum mechanical calculations including configuration interaction.
Journal ArticleDOI
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
TL;DR: In this article, a large number of mainly nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series are discussed and the theoretical properties of the sequence transformations in convergence acceleration and summation processes are analyzed.
Posted Content
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
TL;DR: In this report, a large number of mainly nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series are discussed and efficient algorithms for the evaluation of these transformations are derived.
Journal ArticleDOI
Extrapolation methods for Sommerfeld integral tails
TL;DR: In this article, a review of the extrapolation methods for accelerating the convergence of Sommerfeld-type integrals is presented, which arise in problems involving antennas or scatterers embedded in planar multilayered media.
Journal ArticleDOI
A general extrapolation algorithm
TL;DR: A general formalism for linear and rational extrapolation processes is developped, which includes most of the sequence transformations actually used for convergence acceleration.
References
More filters
Journal ArticleDOI
Non‐linear Transformations of Divergent and Slowly Convergent Sequences
TL;DR: In this article, a family of non-linear sequence-to-sequence transformations, ek, ekm, ẽk, and ed, are discussed and a brief history of the transformations is related and a simple motivation for the transforms is given.
Journal ArticleDOI
Computation of the padé table
TL;DR: Simple recursion formulas are presented for computing the coefficients in the Pade table of a power series f(x) and a Fortran subroutine for the computation is given in an Appendix.
Journal ArticleDOI
Tables for the rapid and accurate numerical evaluation of certain infinite integrals involving Bessel functions
TL;DR: In this article, a Fourier integral solution for the plane-stress problem of a circular ring with concentrated radial loads is presented, where the number of stresses in a notched strip under tension is a function of the radius of the circle.