Nonlinear transformations for accelerating the convergence of -dimensional series

Authors:
N. C. Albertsen, G. Jacobsen and S. B. Sørensen

Journal:
Math. Comp. **41** (1983), 623-634

MSC:
Primary 65B10

MathSciNet review:
717708

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Abstract | References | Similar Articles | Additional Information

Abstract: Two transformations for accelerating the convergence of infinite *M*-dimensional series are presented. They are generalizations of Shanks' *e*-transformation and Levin's one-dimensional transformations, respectively.

**[1]**George A. Baker Jr.,*Essentials of Padé approximants*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR**0454459****[2]**Claude Brezinski,*Accélération de la convergence en analyse numérique*, Lecture Notes in Mathematics, Vol. 584, Springer-Verlag, Berlin-New York, 1977 (French). MR**0455266****[3]**J. S. R. Chisholm,*Rational approximants defined from double power series*, Math. Comp.**27**(1973), 841–848. MR**0382928**, 10.1090/S0025-5718-1973-0382928-6**[4]**J. S. R. Chisholm and J. McEwan,*Rational approximants defined from power series in 𝑁 variables*, Proc. Roy. Soc. (London) Ser. A**336**(1974), 421–452. MR**0361572****[5]**P. R. Graves-Morris, R. Hughes Jones, and G. J. Makinson,*The calculation of some rational approximants in two variables*, J. Inst. Math. Appl.**13**(1974), 311–320. MR**0375739****[6]**David Levin,*On accelerating the convergence of infinite double series and integrals*, Math. Comp.**35**(1980), no. 152, 1331–1345. MR**583511**, 10.1090/S0025-5718-1980-0583511-3**[7]**David Levin,*Development of non-linear transformations of improving convergence of sequences*, Internat. J. Comput. Math.**3**(1973), 371–388. MR**0359261****[8]**Daniel Shanks,*Non-linear transformations of divergent and slowly convergent sequences*, J. Math. and Phys.**34**(1955), 1–42. MR**0068901****[9]**Roland F. Streit,*The evaluation of double series*, Nordisk Tidskr. Informationsbehandling (BIT)**12**(1972), 400–408. MR**0365992****[10]**P. Wynn,*On a device for computing the 𝑒_{𝑚}(𝑆_{𝑛}) tranformation*, Math. Tables Aids Comput.**10**(1956), 91–96. MR**0084056**, 10.1090/S0025-5718-1956-0084056-6

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0717708-9

Article copyright:
© Copyright 1983
American Mathematical Society