Fast and stable global interpolation based on equidistant points

TL;DR

This paper introduces a symmetric wave interpolation method that achieves stable, accurate global interpolation using equidistant points, effectively overcoming the Runge phenomenon and matching Chebyshev interpolation performance.

Contribution

It presents a novel symmetric wave interpolation technique that combines the practicality of equidistant points with the numerical stability typically associated with Chebyshev interpolation.

Findings

Effectively suppresses Runge phenomenon

Achieves accuracy comparable or superior to Chebyshev interpolation

Provides a practical solution for stable global interpolation

Abstract

This paper presents the symmetric wave interpolation method for stable global interpolation using readily available equidistant points. Its key achievement is the integration of the practical utility of such points with the numerical stability of Chebyshev interpolation. Experimental results demonstrate that symmetric wave interpolation effectively suppresses the Runge phenomenon and, crucially, delivers accuracy that matches or even surpasses Chebyshev interpolation. This work thereby provides a robust and practical solution that bridges the long-standing gap between point accessibility and numerical stability in global interpolation.