We study a reliable pole selection for the rational approximation of the resolvent of fractional powers of operators in both the finite and infinite dimensional setting. The analysis exploits the representation in terms of hypergeometric functions of the error of the Padé approximation of the fractional power. We provide quantitatively accurate error estimates that can be used fruitfully for practical computations. We present some numerical examples to corroborate the theoretical results. The behavior of rational Krylov methods based on this theory is also presented.

中文翻译：

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算子分数幂解的Padé型逼近

我们研究了一个可靠的极点选择，用于在有限维和无穷维设置中合理解算算子的分数幂。该分析利用分数幂的Padé逼近误差的超几何函数表示法。我们提供定量准确的误差估计，可以有效地用于实际计算。我们提供一些数值例子来证实理论结果。还介绍了基于该理论的有理Krylov方法的行为。