Error estimates for Riemann sums of some singular functions
Pavel Gurevich, Sergey Tikhomirov
TL;DR
This paper provides error estimates for Riemann sums when applied to certain singular functions, enhancing understanding of numerical integration in challenging cases.
Contribution
It introduces new error bounds specifically for Riemann sums of singular functions, which were not previously well-characterized.
Findings
Derived explicit error estimates for specific singular functions
Improved accuracy understanding for numerical integration of singular functions
Applicable to functions with certain types of singularities
Abstract
In this short note, we obtain error estimates for Riemann sums of some singular functions.
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
TopicsDifferential Equations and Boundary Problems · Mathematical Approximation and Integration · Analytic Number Theory Research