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More quadratically converging algorithms for π

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posted on 2025-05-09, 08:45 authored by J. M. Borwein, P. B. Borwein
We present a quadratically converging algorithm for π based on a formula of Legendre's for complete elliptic integrals of modulus sin(π/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 π.

History

Journal title

Mathematics of Computation

Volume

46

Issue

173

Pagination

247-253

Publisher

American Mathematical Society

Language

  • en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Mathematical and Physical Sciences

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