A convergence and stability study of the iterated Lubkin transformation and the algorithm
Author:
Avram Sidi
Journal:
Math. Comp. 72 (2003), 419433
MSC (2000):
Primary 65B05, 65B10, 40A05, 40A25, 41A60
Published electronically:
May 1, 2002
MathSciNet review:
1933829
Fulltext PDF Free Access
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Abstract: In this paper we analyze the convergence and stability of the iterated Lubkin transformation and the algorithm as these are being applied to sequences whose members behave like as , where and are complex scalars and is a nonnegative integer. We study the three different cases in which (i) , , and (logarithmic sequences), (ii) and (linear sequences), and (iii) (factorial sequences). We show that both methods accelerate the convergence of all three types of sequences. We show also that both methods are stable on linear and factorial sequences, and they are unstable on logarithmic sequences. On the basis of this analysis we propose ways of improving accuracy and stability in problematic cases. Finally, we provide a comparison of these results with analogous results corresponding to the Levin transformation.
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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:
http://dx.doi.org/10.1090/S0025571802014333
PII:
S 00255718(02)014333
Received by editor(s):
March 21, 2001
Published electronically:
May 1, 2002
Article copyright:
© Copyright 2002
American Mathematical Society
