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- W4301473660 abstract "We investigate quasi-Monte Carlo (QMC) integration of bivariate periodic functions with dominating mixed smoothness of order one. While there exist several QMC constructions which asymptotically yield the optimal rate of convergence of $mathcal{O}(N^{-1}log(N)^{frac{1}{2}})$, it is yet unknown which point set is optimal in the sense that it is a global minimizer of the worst case integration error. We will present a computer-assisted proof by exhaustion that the Fibonacci lattice is the unique minimizer of the QMC worst case error in periodic $H^1_text{mix}$ for small $N$. Moreover, we investigate the situation for pointsets whose cardinality $N$ is not a Fibonacci number. It turns out that for $N=1,2,3,5,7,8,12,13$ the optimal point sets are integration lattices." @default.
- W4301473660 created "2022-10-05" @default.
- W4301473660 creator A5024164746 @default.
- W4301473660 creator A5066473999 @default.
- W4301473660 date "2014-09-20" @default.
- W4301473660 modified "2023-10-17" @default.
- W4301473660 title "Optimal point sets for quasi-Monte Carlo integration of bivariate periodic functions with bounded mixed derivatives" @default.
- W4301473660 doi "https://doi.org/10.48550/arxiv.1409.5894" @default.
- W4301473660 hasPublicationYear "2014" @default.
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