Affiliation:
1. Università della Svizzera italiana, Switzerland
Abstract
Barycentric rational interpolation is a recent interpolation method with several favourable properties. In this paper, we present the BRI class, which features a new
C++
class template that contains all variables and functions related to linear barycentric rational interpolation. While several methods exist to evaluate a barycentric rational interpolant, the class is designed to autonomously select the best method to use on a case-by-case basis, as it takes into account the latest results regarding the efficiency and numerical stability of barycentric rational interpolation [
15
]. Moreover, we describe a new technique that makes the code robust and less prone to overflow and underflow errors. In addition to the standard
C++
data types, the BRI template variables can also be defined with arbitrary precision, because the BRI class is compatible with the Multiple Precision Floating-Point Reliable (MPFR) library [
14
].
Publisher
Association for Computing Machinery (ACM)
Reference32 articles.
1. Nikhar Agrawal et al. 2022. BOOST 1.81.0 Library Documentation – Math Toolkit 3.3.0 – Interpolation – Barycentric Rational Interpolation. https://www.boost.org/doc/libs/1_81_0/libs/math/doc/html/math_toolkit/barycentric.html. [Online; accessed 23-February-2023].
2. Time varying ratings in association football: the all-time greatest team is..
3. Rational functions for guaranteed and experimentally well-conditioned global interpolation
4. Jean-Paul Berrut. 2017. Linear barycentric rational interpolation with guaranteed degree of exactness. In Approximation Theory XV: San Antonio 2016, Gregory E. Fasshauer and Larry L. Schumaker (Eds.). Springer International Publishing, Cham, 1–20.
5. The Conditioning of a Linear Barycentric Rational Interpolant