FAU MoD Lecture: Applications of AAA Rational Approximation

Date: Wed. February 1, 2023
Event: FAU MoD Lecture
Organized by: FAU MoD, Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Speaker: Prof. Dr. Nick Trefethen
Affiliation: University of Oxford

This FAU MoD Lecture will have two sessions:

[Session 1] Main lecture (10:30H – 11:30H)
(On-site / online)

Applications of AAA Rational Approximation

Abstract. For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, including
• detection of singularities
• model order reduction
• analytic continuation
• functions of matrices
• nonlinear eigenvalue problems
• interpolation of equispaced data
• smooth extension of multivariate real functions
• extrapolation of ODE and PDE solutions into the complex plane
• solution of Laplace problems
• conformal mapping
• Wiener-Hopf factorization
(joint work with Stefano Costa and others)


[Session 2] (16:30H – 17:30H)

A Tour of Chebfun

By Prof. Dr. Nick Trefethen

This session will be a hands-on introduction to Chebfun, and it should be of interest to anyone who uses MATLAB. Chebfun starts from the idea of continuous analogues of Matlab operations: vectors are overloaded to functions and matrices to operators. The result is an appealing tool for all kinds of problems of rootfinding, quadrature, optimization, and ODEs.

If you wish to play along, bring your laptop and download the software in advance from www.chebfun.org or https://github.com/chebfun/chebfun/.



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You might like:
New Algorithms in MATLAB. Invitation to FAU MoD Lecture by Prof. Dr. Nick Trefethen at the Faculty of Sciences at FAU (English version)
Neue Algorithmen in MATLAB. Einladung zu Fachvorträgen von Prof. Dr. Nick Trefethen am 1. Februar 2023 (German version)
• FAU MoD Lecture: Learning-Based Optimization and PDE Control in User-Assignable Finite Time by Prof. Dr. Miroslav Krstic

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// Photo of Prof. Trefethen by Sarah Bird