Analysis of convergence of the transformation for power series
Author:
Avram Sidi
Journal:
Math. Comp. 35 (1980), 833850
MSC:
Primary 41A60; Secondary 40A05, 40A25, 41A25
MathSciNet review:
572860
Fulltext PDF Free Access
Abstract 
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Abstract: Recently the present author has given some convergence theorems of general nature for Levin's nonlinear sequence transformations. In this work these theorems are extended and sharpened to cover the case of power series, both inside and on their circle of convergence. It is shown that one of the two limiting processes considered in the previous work can be used for analytic continuation and a realistic estimate of its rate of convergence is given. Three illustrative examples are also appended.
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 LEVIN & A. SIDI (1975), "Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series," Appl. Math. Comput. (To appear.) MR 650681 (83d:65010)
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 W. J. OLVER (1974), Asymptotics and Special Functions, Academic Press, New York and London. MR 0435697 (55:8655)
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 SHANKS (1955), "Nonlinear transformations of divergent and slowly convergent sequences," J. Math. Phys., v. 34, pp. 142. MR 0068901 (16:961e)
 [A]
 SIDI (1979), "Convergence properties of some nonlinear sequence transformations," Math. Comp., v. 33, pp. 315326. MR 514827 (81h:65003)
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 [I]
 H. SNEDDON (1972), The Use of Integral Transforms, McGrawHill, New York.
 [J]
 WIMP (1977), "New methods for accelerating the convergence of sequences arising in Laplace transform theory," SIAM J. Numer. Anal., v. 14, pp. 194204. MR 0433798 (55:6770)
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 WYNN (1956), "On a device for computing the transformation," MTAC, v. 10, pp. 9196. MR 0084056 (18:801e)
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 WYNN (1956a), "On a procrustean technique for the numerical transformation of slowly convergent sequences and series," Proc. Cambridge Philos. Soc., v. 52, pp. 663671. MR 0081979 (18:478c)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005728600
PII:
S 00255718(1980)05728600
Article copyright:
© Copyright 1980
American Mathematical Society
