The Borwein brothers, Pi and the AGM.

@article{Brent2018TheBB,
  title={The Borwein brothers, Pi and the AGM.},
  author={Richard P. Brent and Richard P. Brent},
  journal={arXiv: Number Theory},
  year={2018}
}
  • R. Brent, R. Brent
  • Published 21 February 2018
  • Computer Science, Mathematics
  • arXiv: Number Theory
We consider some of Jonathan and Peter Borweins' contributions to the high-precision computation of $\pi$ and the elementary functions, with particular reference to their book "Pi and the AGM" (Wiley, 1987). Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM converges quadratically, it can be combined with fast multiplication algorithms to give fast algorithms for the {$n$-bit} computation of $\pi$, and more generally the elementary functions. These algorithms… 
1 Citations

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