- CARMA SEMINAR
- Speaker: Prof. Richard Brent, Australian National University
- Title: Jonathan Borwein and Pi
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 1:59 pm, Wed, 14th Mar 2018
- Abstract:
The late Professor Jonathan Borwein was fascinated by the constant
$\pi$. Some of his talks on this topic can be found on the CARMA website.
This homage to Jon is based on my talk at the Jonathan Borwein Commemorative
Conference. I will describe some algorithms for the high-precision
computation of $\pi$ and the elementary functions, with particular reference
to the book Pi and the AGM by Jon and his brother Peter Borwein.
Here "AGM" is the arithmetic-geometric mean
of Gauss and Legendre. Because the AGM has second-order convergence, it
can be combined with FFT-based fast multiplication algorithms to give fast
algorithms for the \hbox{$n$-bit} computation of $\pi$.
I will survey a few of the results and algorithms that were of interest to
Jon. In several cases they were either discovered or improved by him. If
time permits, I will also mention some new results that would have been of
interest to Jon.
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