Numerical Continued Fraction Interpolation

TL;DR

This paper introduces a greedy method for constructing Thiele interpolating continued fractions that achieves high accuracy, comparable to advanced rational interpolation techniques, with potential improvements in efficiency.

Contribution

It presents a novel greedy selection and early termination approach for Thiele continued fractions, enhancing approximation accuracy and computational efficiency.

Findings

Achieves high-accuracy approximations with the proposed method.

Comparable results to state-of-the-art rational interpolation techniques.

Demonstrates effectiveness of greedy selection and early termination in continued fractions.

Abstract

We show that highly accurate approximations can often be obtained from constructing Thiele interpolating continued fractions by a Greedy selection of the interpolation points together with an early termination condition. The obtained results are comparable with the outcome from state-of-the-art rational interpolation techniques based on the barycentric form.