Marcus Webb - Beyond Chebyshev Technology
|Dates:||25 October 2019|
|Times:||14:00 - 15:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Marcus Webb will be speaking at this seminar.
Abstract : Chebfun is a MATLAB software package for computing numerically with functions, whose inner workings boil down essentially to approximating functions by Chebyshev polynomial expansions. In this talk we’ll discuss problems in which Chebyshev polynomials are not the best basis to use, necessitating the transformation to other bases such as Legendre and other Jacobi polynomials (and back again to Chebyshev). The main part of the talk will be on the state-of-the-art algorithm for transforming between different families of Jacobi polynomials, due to Townsend, myself, and Olver (https://doi.org/10.1090/mcom/3277), which involves Toeplitz matrices, Hankel matrices, low-rank matrix approximation, and the FFT. The analysis involves some rational approximation problems of Zolotarev (https://doi.org/10.1137/19M1244433). We conclude with interesting related miscellanea.
Organisation: The University of Manchester
Travel and Contact Information
Frank Adams 1
Alan Turing Building