Work

Stable evaluation of derivatives for barycentric and continued fraction representations of rational functions

Year: 2026

Type: article

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.

Source: Research in the Mathematical Sciences

DOI: 10.1007/s40687-026-00655-6

Authors: Tobin A. Driscoll, Yuxing Zhou

Institution: University of Delaware

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,090

OpenAlex ID: W7124446851