The Even-Rho and Even-Epsilon Algorithms for Accelerating Convergence of a Numerical Sequence

Abstract

Two closely related algorithms are presented for extrapolating to the limit of a scalar sequence. One, the even-epsilon algorithm, is due to Wynn; it permits systematic calculation of the array of Shank's transforms or, equivalently, of the related Pade Table. The other, the even-rho algorithm, is closely related to the first and is also based on Wynn's work; however, it has different properties and has not enjoyed the same theoretical development. Singular rules and near-singular rules are developed for both algorithms to handle situations in which adjacent tabular entries are equal or nearly equal, leading to zero or very small divisors. Computer programs implementing these algorithms are given along with sample output. An appreciable amount of historical background material is included. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA109445

Entities

People

  • Robert P. Eddy

Tags

Communities of Interest

  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computations
  • Computer Programs
  • Computers
  • Equations
  • Extrapolation
  • Materials
  • Mathematics
  • New York
  • Numerical Analysis
  • Ordnance Laboratories
  • Power Series
  • Procedures (Computers)
  • Rational Functions
  • Sequences
  • Three Dimensional

Readers

  • Approximation Theory.
  • Systems Analysis and Design