Past Event: SIAM Speaker Series

Continuous Linear Algebra and Chebfun

Nick Trefethen, Professor, Numerical Analysis and head of the Numerical Analysis Group, Oxford University

Abstract

Linear algebra deals with discrete vectors and matrices, and MATLAB was built on giving easy access to these structures and the best algorithms for working with them. But almost everything in linear algebra has a continuous analogue, where vectors become functions and matrices become operators. The Chebfun project develops this analogy with mathematics, algorithms, and software, and the talk will present ideas and Chebfun demonstrations in areas including matrix factorizations, complex variables, differential equations, and data science. Once you start thinking and computing this way, it's hard to go back. Bio Nick Trefethen is a Professor of Numerical Analysis and head of the Numerical Analysis Group at Oxford University. His work spans numerous areas including pseudospectra for non-normal matrices, spectral methods, numerical linear algebra, fluid mechanics, and approximation theory. He was educated at Harvard and Stanford and held positions at NYU, MIT, and Cornell before moving to Oxford in 1997. He is a Fellow of the Royal Society and a member of the US National Academy of Engineering and served during 2011-2012 as President of SIAM. He has won many prizes including the IMA Gold Medal of the Institute for Mathematics and its Applications, the Naylor Prize of the London Mathematical Society, and the Polya and von Neumann Prizes from SIAM. He holds honorary doctorates from the University of Fribourg and Stellenbosch University. As an author, Trefethen is known for his books including Numerical Linear Algebra (1997), Spectral Methods in MATLAB (2000), Spectra and Pseudospectra (2005), Approximation Theory and Approximation Practice (2013/2019), and Exploring ODEs (2018). He organized the SIAM 100-Dollar, 100-Digit Challenge in 2002 and is the inventor of Chebfun. (The SIAM Distinguished Seminar Series aims to host accomplished researchers to talk about an insightful topic of their choice to help researchers both in terms of research and life in general.)