Recent Advances in Algorithms for Rational Minimax Approximations

Explore cutting-edge algorithmic developments in rational minimax approximations through this 52-minute conference talk presented at ICBS2025 by BIMSA. Delve into the latest theoretical breakthroughs and computational methods for finding optimal rational approximations that minimize the maximum error over a given interval or domain. Learn about state-of-the-art algorithms that address the challenges of non-convex optimization inherent in rational approximation problems, including techniques for handling poles, convergence issues, and numerical stability. Discover how these advances impact applications in scientific computing, signal processing, and numerical analysis where high-precision approximations of complex functions are essential. Gain insights into the mathematical foundations underlying these algorithms, their computational complexity, and practical implementation considerations for solving real-world approximation problems.