Approximation Theory and Spline Functions pp 247-256
Explicit Algebraic Nth Order Approximations to PI
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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- 1.Borwein, J. M., and Borwein, P. B., “Cubic and higher order algorithms for π”, to appear, Canad. Math. Bull.Google Scholar
- 2.Borwein, J. M., and Borwein, P. B., “Elliptic integral and approximation of π’. Preprint.Google Scholar
- 3.Borwein, J. M., and Borwein, P. B., “The arithmetic-geometric mean and fast computation of elementary functions”, SIAM Review, 26, 1984.Google Scholar
- 7.Salarnin, E., “Computation of π using arithmetic-geometric mean”, Math. Comput. 135, 1976, pp. 565–570.Google Scholar
- 8.Tamura, Y., and Kanada, Y., “Calculation of π to 4, 196, 293 decimals based on Gauss-Legendre algorithm”, preprint.Google Scholar