We describe an adaptive greedy algorithm for Thiele continued-fraction approximation of a function defined on a continuum domain in the complex plane. The algorithm iteratively selects interpolation nodes from an adaptively refined set of sample points on the domain boundary. We also present new algorithms for evaluating Thiele continued fractions and their accessory weights using only a single floating-point division. Numerical experiments comparing the greedy TCF method with the AAA algorithm on several challenging functions defined on the interval $[-1,1]$ and on the unit circle show that continuum TCF is consistently 2.5 to 8 times faster than AAA.

翻译：本文描述了一种自适应贪婪算法，用于复平面上连续域定义函数的Thiele连分式逼近。该算法从域边界自适应细化的采样点集中迭代选择插值节点。我们还提出了仅需单次浮点除法即可计算Thiele连分式及其附属权值的新算法。在区间$[-1,1]$和单位圆上若干挑战性函数的数值实验中，将贪婪TCF方法与AAA算法进行比较，结果表明连续域TCF算法的计算速度始终达到AAA算法的2.5至8倍。