Abstract
We present a family of algorithms for computing pi which converge with order m (m any integer larger than one). Details are given for two, three and seven.
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Borwein, J. M., and Borwein, P. B., “Cubic and higher order algorithms for π”, to appear, Canad. Math. Bull.
Borwein, J. M., and Borwein, P. B., “Elliptic integral and approximation of π’. Preprint.
Borwein, J. M., and Borwein, P. B., “The arithmetic-geometric mean and fast computation of elementary functions”, SIAM Review, 26, 1984.
Brent, R. P., “Fast multiple-precision evaluation of elementary functions”, J. Assoc. Comput. Mach. 23, 1976, pp. 242–251.
Cayley, A., “An elementary treatise on elliptic functions”, Bell and Sons, 1895, republished Dover 1961.
Cayley, A., “A memoir on the transformation of elliptic functions”, Phil. Trans. T., 164, 1874, pp. 397–456.
Salarnin, E., “Computation of π using arithmetic-geometric mean”, Math. Comput. 135, 1976, pp. 565–570.
Tamura, Y., and Kanada, Y., “Calculation of π to 4, 196, 293 decimals based on Gauss-Legendre algorithm”, preprint.
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© 1984 D. Reidel Publishing Company
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Borwein, J.M., Borwein, P.B. (1984). Explicit Algebraic Nth Order Approximations to PI. In: Singh, S.P., Burry, J.W.H., Watson, B. (eds) Approximation Theory and Spline Functions. NATO ASI Series, vol 136. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6466-2_12
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DOI: https://doi.org/10.1007/978-94-009-6466-2_12
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-94-009-6466-2
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