Alex Townsend
 Alex TownsendMmath
eMail:
Alex [dot] Townsend [-at-] maths [dot] ox [dot] ac [dot] uk
Reception/Secretary: +44 1865 273525 Office: RI.0.55 Preferred Address:townsend AT maths.ox.ac.uk Departmental Address:
Mathematical Institute |
Research Interests:
I have worked on the theory of Radial Basis Functions (RBFs) related to the multilevel algorithm on bounded domains and various RBF inequalities. This research accommodates arbitrarily high dimensions though in practice we used it only for 2D ! A year into my research I changed supervisors because my first supervisor left Oxford. I now work on neoclassical approximation theory, spectral methods and two dimensional spectral approximations. My main focus hops between these three themes and that makes my research life fun. I am also an active member of the Chebfun team and have written a software package called Chebfun2 (Chebfun in two dimensions). An alpha version of Chebfun2 is publicly available here. Here is MATLAB code to construct the basic ultraspherical spectral operators: BasicUltraops.m. Below are three images from my research:
Please feel free to email me if you have any questions related to my research. Prizes, Awards and Scholarships:
SIAM UKIE prize for the best student talk at the 24th Biennial Numerical Analysis conference in Strathclyde. IMA prize in 2010 for outstanding examination results. Junior Maths Prize in 2009 for outstanding examination results. College scholarship for outstanding examination results. Major/Recent Publications:
A. Townsend & L. N. Trefethen, An extension of Chebfun to two dimensions, submitted. pdf A. Townsend, V. Noferini & Y. Nakatsukasa, Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach, submitted. pdf A. Townsend & L. N. Trefethen, Gaussian elimination as an iterative algorithm, SIAM News, March 2013. pdf N. Hale & A. Townsend, Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights, SISC, 35 (2013), A652-A672. pdf S. Olver & A. Townsend, A fast and well-conditioned spectral method, (2012), arXiv:1202.1347v2, to appear in SIAM Review. pdf A. Townsend & H. Wendland, Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values, to appear in IMA J. Numer. Anal. pdf Teaching:
Graduate Teaching Assistant for New college (2012-2013). Taught Numerical Linear Algebra and Numerical Analysis in 2011 & 2012. Further Details:
Selected Talks: Chebfun2: Exploring constant coefficient PDEs on rectangles (2013). pdf Chebfun: Numerical computing with functions (2013). [An invited 1hr 40min tutorial] pdf Double ansatz spaces and barycentric rootfinding (2012). pdf Chebfun2: Bivariate function approximation the ACA way (2012). pdf Computing Gauss-Jacobi quadrature rules (2012). pdf A fast and well-conditioned spectral method (2012). pdf Multiscale analysis on bounded domains with restricted interpolation points (2011). [Awarded SIAM UKIE best student talk prize] pdf Other Activities I am also a very keen (perhaps too keen) squash player and regularly play in box leagues and for Oxford University Club. |
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