Chebyshev to Zolotarev, Faber to Ganelius, and EIM to AAA – Alex Townsend (Cornell University)

December 9, 2019 @ 1:30 pm – 2:00 pm
Seminar Room 1
Newton Institute

In 1854, Chebyshev derived the Chebyshev polynomials via a minimax polynomial problem. About 20 years later, Zolotarev (a student in one of Chebyshev's courses) generalized the minimax problem to one involving rational functions. These minimax problems are now used to understand the convergence behavior of Krylov methods, the decay rate of singular values of structured matrices, and the development of fast PDE solvers. In this talk, we will survey the computational complex analysis techniques that can be used to solve Chebyshev's and Zolotarev's minimax problems and try to highlight the ongoing connections between polynomials and rationals.