On a Bivariate Generalization of Berrut’s Barycentric Rational Interpolation to a Triangle

Len Bos,Stefano De Marchi

doi:10.3390/math9192481

Abstract

We discuss a generalization of Berrut’s first and second rational interpolants to the case of equally spaced points on a triangle in R2.

Highlights

Berrut [1,2,3] introduced two versions of a univariate rational interpolation procedure that has proven to be efficient and effective, even for spaced points in an interval.Of note is that the complexity of these procedures is linear in the number of points
The derivation of these procedures is based on the classical Whittaker–Shannon sampling theorem [4,5,6])
For any linear interpolant it is possible, by means of a so-called Boolean sum, to create a hybrid version that reproduces any specifed finite dimensional subspace of functions, the most common example of such being the space of polynomials of degree one

Summary

Introduction

Berrut [1,2,3] introduced two versions of a univariate rational interpolation procedure that has proven to be efficient and effective, even for spaced points in an interval.Of note is that the complexity of these procedures is linear in the number of points. Abstract: We discuss a generalization of Berrut’s first and second rational interpolants to the case of spaced points on a triangle in R2 . The cases of d = 0, 1 correspond to Berrut’s first and second interpolants, respectively.

Results

Conclusion