A new rational approximation algorithm via the empirical interpolation method
Numerical Analysis
2025-01-23 v3 Numerical Analysis
Abstract
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for space-fractional differential equations, parameter-robust preconditioning, and evaluation of matrix functions. Compared to classical rational approximation algorithms, the proposed method is more efficient for approximating a large number of target functions. In addition, we derive a convergence estimate of our rational approximation algorithm using the metric entropy numbers. Numerical experiments are included to demonstrate the effectiveness of the proposed method.
Cite
@article{arxiv.2406.19339,
title = {A new rational approximation algorithm via the empirical interpolation method},
author = {Aidi Li and Yuwen Li},
journal= {arXiv preprint arXiv:2406.19339},
year = {2025}
}