In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a set valued variant of the Adaptive Antoulas Anderson (AAA) algorithm. It builds on the Set-Valued AAA framework from [16], accelerating it by using an approximate orthogonal basis obtained from a truncated QR decomposition. We demonstrate both theoretically and numerically this method's robustness. We show how it can be parallelized while maintaining the desired accuracy, with minimal communication cost.

翻译：本文提出了一种快速且可并行化的有理逼近算法。该方法被称为(P)QR-AAA，是自适应Antoulas Anderson（AAA）算法的集值变体。它建立在文献[16]提出的集值AAA框架基础上，通过利用截断QR分解获得的近似正交基来加速该框架。我们从理论和数值两方面证明了该方法的鲁棒性。同时展示了该方法在保持所需精度的前提下如何实现并行化，且通信开销极低。