Acceleration of Series,

Abstract

The rate of convergence of infinite series can be accelerated by a suitable splitting of each term into two parts and then combining the second part of the n-th term with the first part of the (n+1)-th term to get a new series and leaving the first part of the first term as an 'orphan'. Repeating this process an infinite number of times, the series will often approach zero, and one obtains the series of orphans, which may converge faster than the original series. Heuristics for determining the splits are given.

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1974
Accession Number
ADA011837

Entities

People

  • R. W. Gosper

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Convergence
  • Infinite Series
  • Mathematical Analysis
  • Mathematics
  • Motion
  • Physical Properties
  • Sequences
  • Splitting

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Statistical inference.