12:30–1:30 pm
Jones 303 5747 S. Ellis Avenue
Kingsley Yeon
Committee on Computational and Applied Mathematics
The University of Chicago
"Deep Univariate Polynomial and Conformal Approximation"
Abstract
We present a novel approach in approximation theory, which involves approximating a univariate function using deep polynomial approximations. Inspired by the success of deep neural networks, a deep approximation is defined as a composite function composed of multiple layers of simple functions. We will elucidate the theoretical underpinnings of this approach by examining its effectiveness in mitigating the Runge phenomenon and exploring the serpentine properties of deep approximations. Moreover, our computational experiments, incorporating two and three polynomial layers, demonstrate that this methodology yields more accurate approximations compared to a single polynomial with an equivalent number of degrees of freedom (coefficients).