Journal Article

A general approach to the construction of convergence acceleration methods for vector sequences is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stabililty properties of the topological epsilon algorithm are likewise given.

Full Text

Duke Authors

Cited Authors

  • Sidi, A; Ford, WF; Smith, DA

Published Date

  • January 1, 1986

Published In

Volume / Issue

  • 23 / 1

Start / End Page

  • 178 - 196

International Standard Serial Number (ISSN)

  • 0036-1429

Digital Object Identifier (DOI)

  • 10.1137/0723013

Citation Source

  • Scopus