Asymptotic analysis of a generalized Richardson extrapolation process on linear sequences

Author:
Avram Sidi

Journal:
Math. Comp. **79** (2010), 1681-1695

MSC (2000):
Primary 40A05, 40A25, 41A60, 65B05, 65B10

DOI:
https://doi.org/10.1090/S0025-5718-09-02318-7

Published electronically:
November 30, 2009

MathSciNet review:
2630007

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Abstract: In this work, we give a detailed convergence and stability analysis for the author's generalized Richardson extrapolation process GREP as this is being applied to linearly convergent or divergent infinite sequences , where as , being distinct. The quantity we would like to compute is , whether it is the limit or antilimit of . Such sequences arise, for example, as partial sums of power series and of Fourier series of functions that have algebraic and/or logarithmic branch singularities. Specifically, we define the GREP approximation to , with and , via the linear systems

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Additional Information

**Avram Sidi**

Affiliation:
Computer Science Department, Technion, Israel Institute of Technology, Haifa 32000, Israel

Email:
asidi@cs.technion.ac.il

DOI:
https://doi.org/10.1090/S0025-5718-09-02318-7

Keywords:
Acceleration of convergence,
generalized Richardson extrapolation process,
GREP$^{(m)}$,
power series,
Fourier series,
asymptotic expansions.

Received by editor(s):
April 30, 2009

Received by editor(s) in revised form:
June 25, 2009

Published electronically:
November 30, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.