European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
17:30   Zuiderduinzaal: Keynote: Michele Benzi, Scuola Normale Superiore, Italy
45 mins
Some uses of the field of values in numerical analysis
Michele Benzi
Abstract: In this expository talk I will show how the field of values (or numerical range) of an operatorcan be used to investigate certain problems involving non-normal matrices. In particular, I willdiscuss decay properties and polynomial approximation of functions of large matrices, andhow to estimate the rate of convergence of preconditioned iterative methods for solving thesaddle point problems arising from the discretization of systems of PDEs like the coupled Stokes-Darcy equations. I will also briefly discuss Crouzeix’s conjecture, undoubtedly the most intriguing openproblem in matrix theory.