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Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen. (German) Zbl 0291.65002

MSC:
65B05 Extrapolation to the limit, deferred corrections
65D30 Numerical integration
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References:
[1] Bulirsch, R., Stoer, J.: Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus. Numer. Math.6, 413-427 (1964) · Zbl 0123.32101
[2] Elsner, L.: Zur Richardson-Extrapolation bei der Simpsonschen Integrationsformel. ZAMM46, T47-T48 (1966) · Zbl 0143.38705
[3] Fox, L.: Romberg integration for a class of singular integrands. Computer J.10, 87-93 (1967) · Zbl 0158.16001
[4] Joyce, D. C.: Survey of extrapolation processes in numerical analysis. SIAM Review13, 435-490 (1971) · Zbl 0229.65005
[5] Lyness, J. N.: Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature. Math. Comp.25, 87-104 (1971) · Zbl 0217.52501
[6] Lyness, J. N., Ninham, B. W.: Numerical quadrature and asymptotic expansions. Math. Comp.2, 162-178 (1967) · Zbl 0178.18402
[7] Miller, J. C. P.: Neville’s and Romberg’s processes: a fresh appraisal with extensions. Philos. Trans. Roy. Soc. London Ser. A263, 525-562 (1968) · Zbl 0176.14301
[8] Oliver, J.: The efficiency of extrapolation methods for numerical integration. Numer. Math.17, 17-32 (1971) · Zbl 0198.21102
[9] Richardson, C., Gaunt, J.: The deferred approach to the limit. Trans. Roy. Soc. London226, 300-361 (1927) · JFM 53.0432.02
[10] Stetter, H.-J.: Analysis of discretization methods for ordinary differential equations. 1. Aufl. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0276.65001
[11] Stoer, J.: Einführung in die Numerische Mathematik I. 1. Aufl. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0245.65001
[12] Uspensky, J. V.: On the expansion of the remainder in Newton-Cotes formula. Trans. Amer. Math. Soc.37, 381-396 (1935) · Zbl 0011.34302
[13] Waterman, P. C., Yos, J. M., Abodeely, R. J.: Numerical integration of nonanalytic functions. J. Math. Phys.43, 45-50 (1964) · Zbl 0221.65039
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