Stable evaluation of derivatives for barycentric and continued fraction representations of rational functions
Abstract
Abstract Effective algorithms for approximation by rational functions exist for both barycentric and Thiele continued fraction (TCF) representations. We present the first numerically stable methods for derivative evaluation in the barycentric representation, including an O ( n ) algorithm for all derivatives. We also extend an earlier O ( n ) algorithm for evaluation of the TCF first derivative to higher orders. Numerical experiments confirm the robustness and efficiency of the proposed methods.
Fields of Study & Subjects
Mathematical functions and polynomials
Mathematical and Computational Methods
Polynomial and algebraic computation
Publication details
- Journal / source
- Research in the Mathematical Sciences
- Volume
- 13
- Issue
- 3
- Publication date
- 28 August 2026
- Language
- EN