×

On two methods for accelerating convergence of series. (English) Zbl 0518.65001


MSC:

65B10 Numerical summation of series
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Brezinski, C.: Generation de suites totalment monotones et oscillantes. C.R. Acad. Sci. Paris Ser. A280, 729-731 (1975) · Zbl 0302.65091
[2] Dahlquist, G., Björch, Å.: Numerical Methods, Prentice-Hall Series in Automatic Computation. New York: Englewood Cliffs 1974
[3] Gabutti, B.: On high precision methods for computing integrals involving bessel functions. Math. Comp.33, 1049-1057 (1979) · Zbl 0438.65027 · doi:10.1090/S0025-5718-1979-0528057-5
[4] Gabutti, B., Lyness, J.N.: An acceleration method for the power series of entire functions of order 1. Math. Comput.39, 587-597 (1982) · Zbl 0525.65002
[5] Gragg, W.B.: Truncation error bounds forg-fractions. Numer. Math.11, 370-379 (1968) · Zbl 0177.43202 · doi:10.1007/BF02161885
[6] Gustafson, S.-Å.: Convergence acceleration of a general class of power series. Computing21, 53-59 (1978) · Zbl 0403.65002 · doi:10.1007/BF02252194
[7] Hardy, G.H.: Divergent series. Oxford: Clarendon Press 1958 · Zbl 0897.01044
[8] Hausdorff, F.: Summationsmethoden und Momentfolgen. J. mathematische Zeitschrift9, 74-79 (1921) · JFM 48.2005.01 · doi:10.1007/BF01378337
[9] Henrici, P.: Some applications of the quotient-difference algorithm, in: Proc. Symp. Appl. Math. 15 Amer. Math. Soc., Providence, pp. 159-183, 1963 · Zbl 0139.10002
[10] Knopp, K.: Theory and application of infinite series. London: Blackie and Son 1928) · JFM 54.0222.09
[11] Niethammer, W.: Numerical application of Euler’s series transformation and its generalizations. Numer. Math.34, 271-283 (1980) · Zbl 0422.65002 · doi:10.1007/BF01396703
[12] Scraton, R.E.: A note on the summation of divergent power series. Proc. Camb. Philos. Soc.66, 109-114 (1969) · Zbl 0174.11603 · doi:10.1017/S0305004100044765
[13] Streit, R.F.: TheT +m Transformation. Math. Comput.30, 505-511 (1976) · Zbl 0332.65001
[14] Titchmarsh, M.A.: The theory of functions. London: Oxford University Press 1947 · Zbl 0032.15605
[15] Wall, H.S.: Continued fractions and totally monotone sequences. Trans. Amer. Math. Soc.48, 165-184 (1940) · Zbl 0024.21602 · doi:10.1090/S0002-9947-1940-0002642-0
[16] Wynn, P.: A note on the generalized Euler transformation. Comput. J.14, 437-441 (1971) · Zbl 0227.65002 · doi:10.1093/comjnl/14.4.437
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.