Optimal Algorithms for Numerical Integration: Recent Results and Open Problems
Erich Novak
TL;DR
This paper reviews recent advances in optimal algorithms for numerical integration, discusses theoretical bounds, universality, and applications to various domains, and highlights open problems for future research.
Contribution
It provides a comprehensive overview of recent results and open problems in the development of optimal numerical integration algorithms.
Findings
Established new lower bounds for integration accuracy
Explored universality properties of algorithms
Extended results to general domains and iid information
Abstract
We present recent results on optimal algorithms for numerical integration and several open problems. The paper has six parts: 1. Introduction 2. Lower Bounds 3. Universality 4. General Domains 5. iid Information 6. Concluding Remarks
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Mathematical Approximation and Integration