Nonlinear transformations for accelerating the convergence of dimensional series
Authors:
N. C. Albertsen, G. Jacobsen and S. B. Sørensen
Journal:
Math. Comp. 41 (1983), 623634
MSC:
Primary 65B10
MathSciNet review:
717708
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Abstract: Two transformations for accelerating the convergence of infinite Mdimensional series are presented. They are generalizations of Shanks' etransformation and Levin's onedimensional transformations, respectively.
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 [2]
 C. Brezinski, Accélération de la Convergence en Analyse Numérique, Lecture Notes in Math. Vol. 584. SpringerVerlag, Berlin and New York, 1977. MR 0455266 (56:13505)
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 J. S. R. Chisholm, "Rational approximants defined from double power series," Math. Comp., v. 27, 1973, pp. 841848. MR 0382928 (52:3810)
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 J. S. R. Chisholm & J. McEwan, "Rational approximants defined from power series in N variables," Proc. Roy. Soc. (London) Ser. A, v. 336, 1974, pp. 421452. MR 0361572 (50:14017)
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 D. Shanks, "Nonlinear transformations of divergent and slowly convergent sequences," J. Math. Phys., v. 34, 1955, pp. 142. MR 0068901 (16:961e)
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 R. F. Streit, "The evaluation of double series," BIT, v. 12, 1972, pp. 400408. MR 0365992 (51:2244)
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 P. Wynn, "On a device for computing the transformation," MTAC, v. 10, 1956, pp. 9196. MR 0084056 (18:801e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307177089
PII:
S 00255718(1983)07177089
Article copyright:
© Copyright 1983
American Mathematical Society
