More quadratically converging algorithms for $\pi$
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- by J. M. Borwein and P. B. Borwein PDF
- Math. Comp. 46 (1986), 247-253 Request permission
Abstract:
We present a quadratically converging algorithm for $\pi$ based on a formula of Legendre’s for complete elliptic integrals of modulus $\sin (\pi /12)$ and the arithmetic-geometric mean iteration of Gauss and Legendre. Precise asymptotics are provided which show this algorithm to be (marginally) the most efficient developed to date. As such it provides a natural computational check for the recent large-scale calculations of $\pi$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Math. Comp. 46 (1986), 247-253
- MSC: Primary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1986-0815846-6
- MathSciNet review: 815846