Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives

DOI10.1007/978-3-319-33507-0_19zbMath1356.65007arXiv1409.5894OpenAlexW2965237500MaRDI QIDQ2957045

Jens Oettershagen, Aicke Hinrichs

Publication date: 20 January 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5894

zbMATH Keywords

numerical examplesFibonacci numberscomputer-assisted proofmultivariate integrationquasi-Monte CarloFibonacci latticebivariate periodic functionsoptimal quadrature points

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (13)

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions ⋮ On the orthogonality of the Chebyshev-Frolov lattice and applications ⋮ Point sets with optimal order of extreme and periodic discrepancy ⋮ A note on the periodic \(L_2\)-discrepancy of Korobov's \(p\)-sets ⋮ Optimal periodic \(L_2\)-discrepancy and diaphony bounds for higher order digital sequences ⋮ On the distribution of the van der Corput sequences ⋮ Extreme and periodic $L_2$ discrepancy of plane point sets ⋮ Improved dispersion bounds for modified Fibonacci lattices ⋮ Extremal distributions of discrepancy functions ⋮ The Role of Frolov's Cubature Formula for Functions with Bounded Mixed Derivative ⋮ Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces ⋮ Uniformly distributed sequences generated by a greedy minimization of the \(L_2\) discrepancy ⋮ Exact order of extreme \(L_p\) discrepancy of infinite sequences in arbitrary dimension

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