CARMA Seminar
1:59 pm
Wednesday, 14th Mar 2018
V205, Mathematics Building
Prof. Richard Brent
(Australian National University)
Jonathan Borwein and Pi
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.