A new rational approximation algorithm via the empirical interpolation method

TL;DR

This paper introduces a novel rational approximation algorithm based on the empirical interpolation method, enhancing efficiency for approximating parametrized functions and solving space-fractional differential equations.

Contribution

The paper proposes a new rational approximation algorithm utilizing the empirical interpolation method, offering improved efficiency and convergence analysis for parametrized functions.

Findings

More efficient than classical methods for many target functions

Provides convergence estimates using metric entropy numbers

Numerical experiments confirm effectiveness

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.