A simple universal algorithm for high-dimensional integration

TL;DR

This paper introduces a straightforward universal algorithm for high-dimensional integration that achieves optimal error rates regardless of dimension, applicable in both randomized and deterministic contexts, supported by theoretical analysis and numerical tests.

Contribution

The paper proposes a novel, simple universal algorithm for high-dimensional integration with optimal error rates across weighted Korobov classes, in both randomized and deterministic settings.

Findings

Achieves dimension-independent optimal error rates

Works in both randomized and deterministic frameworks

Supported by numerical validation

Abstract

We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the randomized and the deterministic setting. Our theoretical findings are complemented by numerical tests.