标题： 计算指数函数的酉最佳逼近 显示英文标题

标题： Computing the unitary best approximant to the exponential function

摘要： 单位虚轴区间上指数函数的最优酉逼近最近已被提出。 在本工作中，考虑了两种算法来计算这个最优逼近：一种基于逐步修正插值节点的有理插值算法，以及AAA-Lawson方法。 此外，引入了后验界来评估计算出的逼近的质量，并在实践中展示收敛到最优酉逼近。 引入了两个先验估计——一个基于实验数据，另一个基于渐近误差估计——以确定最优酉逼近达到给定精度所依赖的频率。 算法和估计的性能通过数值实验进行了验证。 特别是，基于插值的算法在实际中经过少量迭代即可收敛到最优酉逼近。 显示英文摘要

摘要： Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational interpolation in successively corrected interpolation nodes and the AAA-Lawson method. Moreover, a posteriori bounds are introduced to evaluate the quality of a computed approximant and to show convergence to the unitary best approximant in practice. Two a priori estimates -- one based on experimental data, and one based on an asymptotic error estimate -- are introduced to determine the underlying frequency for which the unitary best approximant achieves a given accuracy. Performance of algorithms and estimates is verified by numerical experiments. In particular, the interpolation-based algorithm converges to the unitary best approximant within a small number of iterations in practice.