Fibonacci sets and symmetrization in discrepancy theory
From MaRDI portal
Publication:657648
DOI10.1016/j.jco.2011.07.001zbMath1257.11074OpenAlexW2072179573MaRDI QIDQ657648
Dmitriy Bilyk, Rui Yu, Vladimir N. Temlyakov
Publication date: 10 January 2012
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jco.2011.07.001
Monte Carlo methods (65C05) Numerical integration (65D30) Irregularities of distribution, discrepancy (11K38) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)
Related Items
Star discrepancy subset selection: problem formulation and efficient approaches for low dimensions, An improved lower bound for the \(L_2\)-discrepancy, \(L_{2}\) discrepancy of symmetrized generalized hammersley point sets in base \(b\), On the theorem of Davenport and generalized Dedekind sums, LOWER BOUNDS FOR DISCREPANCY, Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives, Finding exact formulas for the $L_2$ discrepancy of digital $(0,n,2)$-nets via Haar functions, Extreme and periodic $L_2$ discrepancy of plane point sets, Improved dispersion bounds for modified Fibonacci lattices, An exact formula for the \(L_2\) discrepancy of the symmetrized Hammersley point set, Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On obtaining higher order convergence for smooth periodic functions
- A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets
- Symmetrization of the van der Corput generalized sequences
- Cubature formulas, discrepancy, and nonlinear approximation
- Davenport's theorem in the theory of irregularities of point distribution
- Computing discrepancies of Smolyak quadrature rules
- On lower bounds for the \(L_2\)-discrepancy
- The extreme and \(L^2\) discrepancies of some plane sets
- Explicit constructions in the classical mean squares problem in irregularities of point distribution
- Exponential Squared Integrability of the Discrepancy Function in Two Dimensions
- L 2 Discrepancy of Two-Dimensional Digitally Shifted Hammersley Point Sets in Base b
- Harmonic analysis on totally disconnected groups and irregularities of point distributions
- Orthogonality and Digit Shifts in the Classical Mean Squares Problem in Irregularities of Point Distribution
- On irregularities of distribution, III
- On irregularities of distribution, IV
- On irregularities of distribution
- Discrépance et diaphonie en dimension un
- Efficient algorithms for computing the $L_2$-discrepancy
- L2discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations
- Cyclic shifts of the van der Corput set
- A Method for Numerical Integration
- Irregularities of distribution, VII
- On irregularities of distribution
- Note on irregularities of distribution
- Geometric discrepancy. An illustrated guide
- Walsh series analysis of the \(L_2\)-discrepancy of symmetrized point sets