Conversions between barycentric, RKFUN, and Newton representations of\n rational interpolants

2017/11/02 by Steven Elsworth, Stefan Güttel, Elsworth, Steven +1
Computer Science · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1711.00707

openalex publication_date 2017/11/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We derive explicit formulas for converting between rational interpolants in\nbarycentric, rational Krylov (RKFUN), and Newton form. We show applications of\nthese conversions when working with rational approximants produced by the AAA\nalgorithm [Y. Nakatsukasa, O. S `ete, L. N. Trefethen, arXiv preprint\n1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of\nnonlinear eigenvalue problems.\n

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