# An analysis of a butterfly algorithm

## TL;DR

This paper refines the stability analysis of a butterfly algorithm that uses Chebyshev interpolation to efficiently compress oscillatory integral operators, enhancing understanding of its error bounds.

## Contribution

It provides an improved stability analysis of the butterfly algorithm with Chebyshev interpolation, leading to better error estimates.

## Key findings

- Enhanced stability estimates for the butterfly algorithm
- Improved error bounds for oscillatory kernel compression
- Refined analysis supports more reliable application in practice

## Abstract

Butterfly algorithms are an effective multilevel technique to compress discretizations of integral operators with highly oscillatory kernel functions. The particular version of the butterfly algorithm considered here realizes the transfer between levels by Chebyshev interpolation. We present a refinement of the analysis that improves the stability estimates underlying the error bounds.