The Borwein Brothers, Pi and the AGM

DOI10.1007/978-3-030-36568-4_21zbMath1437.11001arXiv1802.07558OpenAlexW2788099209MaRDI QIDQ3298036

Richard P. Brent

Publication date: 21 July 2020

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.07558

zbMATH Keywords

computational complexityquadratic convergencetheta functionslinear convergenceelliptic integralsarithmetic-geometric meanBrent-Salamin algorithmcomputation of \(\pi\)Chudnovsky algorithmquartic convergenceBorwein-Borwein algorithmBorwein-Borwein quartic algorithmequivalence of algorithms for \(\pi\)evaluation of elementary functionsGauss-Legendre algorithmRamanujan-Sato algorithmsSasaki-Kanada algorithm

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Biographies, obituaries, personalia, bibliographies (01A70) Number-theoretic algorithms; complexity (11Y16) History of number theory (11-03) Elliptic functions and integrals (33E05) Evaluation of number-theoretic constants (11Y60) Acceleration of convergence in numerical analysis (65B99)

Uses Software

• Magma

Cites Work

• Even faster integer multiplication
• The arithmetic-geometric mean of Gauss
• The Magma algebra system. I: The user language
• Pi: The Next Generation
• Modern Computer Arithmetic
• Ramanujan's Series for 1/π: A Survey
• The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
• Easy Proofs of Some Borwein Algorithms for π
• More Quadratically Converging Algorithms for &#960
• The Computation of π to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm
• Efficient Multiple-Precision Evaluation of Elementary Functions
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• Fast Multiple-Precision Evaluation of Elementary Functions
• Computation of π Using Arithmetic-Geometric Mean
• The computation of classical constants
• New proofs of Borwein-type algorithms for Pi
• Some Efficient Algorithms for Solving Systems of Nonlinear Equations
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