A Universal Algorithm for Multivariate Integration

2015/07/24 by Krieg, David, Novak, Erich
#65C05 #65D30 #65Y20 #68Q25 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1507.06853

Abstract

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.

Related

• On the Randomization of Frolov's Algorithm for Multivariate Integration
• A simple universal algorithm for high-dimensional integration
• Construction of quasi-Monte Carlo rules for multivariate integration in\n spaces of permutation-invariant functions
• A Random Integration Algorithm for High-dimensional Function Spaces
• A randomized lattice rule without component-by-component construction