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Marcus Webb - Beyond Chebyshev Technology

Dates:25 October 2019
Times:14:00 - 15:00
What is it:Seminar
Organiser:Department of Mathematics
Speaker:Marcus Webb
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  • In category "Seminar"
  • In group "(Maths) Numerical analysis and scientific computing"
  • In group "(Maths) Maths seminar series"
  • By 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.

Speaker

Marcus Webb

Role: Lecturer

Organisation: The University of Manchester

  • https://personalpages.manchester.ac.uk/staff/marcus.webb/default.htm

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Frank Adams 1
Alan Turing Building
Manchester

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Srikara Pranesh

0161 275 5917

srikara.pranesh@manchester.ac.uk

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