BIMSA >
BIMSA Computational Math Seminar
Recent Advances in Algorithms for Rational Minimax Approximations
Recent Advances in Algorithms for Rational Minimax Approximations
Organizers
Zhen Li
,
Xin Liang
,
Zhi Ting Ma
,
Hamid Mofidi
,
Li Wang
,
Fan Sheng Xiong
,
Shuo Yang
,
Wu Yue Yang
Speaker
Lei-Hong Zhang
Time
Thursday, March 20, 2025 3:00 PM - 4:00 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
Rational minimax approximation is a classical topic in approximation theory and is also useful in various applications. Computing the discrete rational minimax approximation in the complex plane is challenging. Due to the development of the adaptive Antoulas-Anderson (AAA) method, rational approximations have received much interest in recent years. However, the computed solutions from the state-of-the-art rational approximation algorithms, such as AAA, AAA-Lawson, and the rational Krylov fitting method, generally are not the minimax approximations. In this talk, we shall offer a new perspective on the rational minimax approximation from the dual side. We will introduce a convex programming approach, the solution of which is guaranteed to be the rational minimax approximation under Ruttan’s condition. Based on this new dual theory, we present a dual-Lawson iteration, and establish its convergence. Numerical results demonstrate that it is a very effective approach for the rational minimax problem, compared to the highly efficient AAA and AAA-Lawson.