Cubature formulas and discrete fourier transform on compact manifolds

TL;DR

This paper develops nearly optimal cubature formulas for compact Riemannian manifolds that are exact for band-limited functions, enhancing numerical integration techniques on curved spaces.

Contribution

It introduces new cubature formulas that are nearly optimal and exact for band-limited functions on compact Riemannian manifolds.

Findings

Formulas are nearly optimal for integration on manifolds.

Exactness for band-limited functions is achieved.

Improves numerical methods on curved spaces.

Abstract

The goal of the paper is to describe essentially optimal cubature formulas on compact Riemannian manifolds which are exact on spaces of band- limited functions.