Rational Empirical Interpolation Methods with Applications
<|reference_start|>Rational Empirical Interpolation Methods with Applications: We present a rational 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.<|reference_end|>
@article{li2024rational,
    title={Rational Empirical Interpolation Methods with Applications},
    author={Aidi Li and Yuwen Li},
    journal={arXiv preprint arXiv:2406.19339},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.19339},
    primaryClass={math.NA cs.NA}
}