[Amath-seminars] Trefethen visit and talks on March 6

Randall J LeVeque rjl at uw.edu
Tue Feb 14 11:33:50 PST 2017


Professor Nick Trefethen from Oxford will be visiting Applied Math on
Monday March 6 and the morning of March 7. I will set up a Google Doc for
those who want to meet with him individually, but in the meantime please
note that he will be giving both a Chebfun demo and a seminar talk on March
6, see below.

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Chebfun Demo
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Speaker: Nick Trefethen, Oxford University

Title: A TOUR OF CHEBFUN, INCLUDING ODEs AND PDEs

Time and Date: 10:30am - 12:00pm on Monday March 6, 2017

Place: Lewis 208 (Wan Conference Room)

Abstract:

Chebfun starts from the idea of continuous analogues of Matlab operations:
vectors are overloaded to functions and matrices to operators. The result
is a beautiful tool for all kinds of problems of rootfinding, quadrature,
optimization, and ODEs. More recently Chebfun has extended much of this
functionality to 2D and 3D, including disks and spheres and
reaction-diffusion equations. Please bring your laptop and download the
software in advance from www.chebfun.org/download/.


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Applied Mathematics Seminar
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Speaker: Nick Trefethen, Oxford University

Title: Cubature, approximation, and isotropy in the hypercube

Time and Date: 4:30pm on Monday March 6, 2017

Place: Smith 102

Abstract:

The hypercube is the standard domain for computation in higher dimensions.
We explore two respects in which the anisotropy of this domain has
practical consequences. The first is the matter of axis-alignment in
low-rank compression of multivariate functions. Rotating a function by a
few degrees in two or more dimensions may change its numerical rank
completely. The second concerns alogrithms based on approximation by
multivariate polynomials, an idea introduced by James Clerk Maxwell.
Polynomials defined by the usual notion of total degree are isotropic, but
in high dimensions, the hypercube is exponentially far from isotropic.
Instead one should work with polynomials of a given "Euclidean degree".
The talk will include numerical illustrations, a theorem based on several
complex variables, and a discussion of "Padua points".


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