 CARMA SEMINAR
 Speaker: Prof. Richard Brent, CARMA, The University of Newcastle
 Title: Jonathan Borwein and Pi
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 1:59 pm, Wed, 14^{th} 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 highprecision
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 arithmeticgeometric mean
of Gauss and Legendre. Because the AGM has secondorder convergence, it
can be combined with FFTbased 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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