A Universal Algorithm for Multivariate Integration
arXiv:1507.0685340 citationsh-index: 33
Originality Highly original
AI Analysis
Provides a single algorithm that is optimal across multiple function spaces, solving a long-standing theoretical problem in numerical integration.
The paper presents a universal algorithm for multivariate integration over cubes that achieves optimal convergence order for both mixed and isotropic Sobolev spaces, unifying previously separate results.
We present an algorithm for multivariate integration over cubes that is unbiased and has optimal order of convergence (in the randomized sense as well as in the worst case setting) for all Sobolev spaces $H^{r, mix}([0,1]^d)$ and $H^s([0,1]^d)$ for $s>d/2$.