# Improved conditioning of the Floater--Hormann interpolants

## TL;DR

This paper introduces a modification to Floater--Hormann rational interpolants by adding local polynomial interpolants at the interval ends, which improves their conditioning and enables higher approximation orders in practical applications.

## Contribution

The paper proposes a new variant of Floater--Hormann interpolants with enhanced conditioning through end-based local polynomial interpolants, facilitating higher approximation accuracy.

## Key findings

- Improved conditioning of interpolants with the proposed modification.
- Enabling higher approximation orders in practical computations.
- Reduction in rounding error amplification.

## Abstract

The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of rounding errors increases with approximation order, and can make balancing the interpolation error and rounding error difficult. This article proposes to modify the Floater--Hormann interpolants by including additional local polynomial interpolants at the ends of the interval. This appears to improve the conditioning of the interpolants and allow higher approximation orders to be used in practice.