Homepage,
Icelandic page,
links,
puzzles.
Research
My advisor is
Steve Vavasis
and with him I'm exploring the numerical solution of polynomial equations.
Specifically, we are looking at algorithms where root finding is
done via eigenvalue problems.
We have a paper on the 1D case:
The two variable case is still very much in the working.
I worked with
Nick Trefethen
before he moved to Oxford.
Among other things, we
explored a cutoff phenomenon for Markov chains.
This is a very neat problem that has been studied by Persi Diaconis
and others.
We mainly looked at two examples, random walk on a
hypercube and riffle shuffling of cards.
In this paper we give a simple formula for the entries of the
transition matrix for riffle shuffling (using the Gilbert-Shannon-Reeds
model), where the states are given by the number of rising sequences.
I have a proof for this formula using only elementary combinatorial
arguments:
I have also done some work on automatic differentiation with
Tom Coleman:
Useful links:
Automatic differentiation:
Programming Languages:
Finite Element Methods:
Other links:
Guðbjörn Freyr Jónsson
jonsson@cam.cornell.edu