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arXiv · 2406.19339

A new rational approximation algorithm via the empirical interpolation method

Aidi Li·Yuwen Li
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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.

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Aidi Li, Yuwen Li. 2024-06-27. A new rational approximation algorithm via the empirical interpolation method. https://arxiv.org/abs/2406.19339

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