Constructions of general polynomial lattices for multivariate integration

DOI10.1017/S0004972700039496zbMath1125.65006MaRDI QIDQ5756325

Peter Kritzer, Friedrich Pillichshammer

Publication date: 4 September 2007

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

algorithmWalsh functionsreproducing kernel Hilbert spacesquasi-Monte Carlo methodLaurent seriescomponent-by-component constructiongenerating vectorpolynomial lattice rulesworst-case integration error

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Random number generation in numerical analysis (65C10) General theory of distribution modulo (1) (11K06) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (4)

Construction algorithms for good extensible lattice rules ⋮ Construction of interlaced scrambled polynomial lattice rules of arbitrary high order ⋮ Construction of scrambled polynomial lattice rules over \(\mathbb{F}_{2}\) with small mean square weighted \(\mathcal{L}_{2}\) discrepancy ⋮ Extensible hyperplane nets

Cites Work

• Point sets and sequences with small discrepancy
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
• The existence of good extensible polynomial lattice rules
• Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
• Constructions of \((t,m,s)\)-nets and \((t,s)\)-sequences
• A class of generalized Walsh functions
• On the step-by-step construction of quasi--Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
• Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Optimal Polynomials for (T,M,S)-Nets and Numerical Integration of Multivariate Walsh Series
• Construction algorithms for polynomial lattice rules for multivariate integration
• Construction Algorithms for Digital Nets with Low Weighted Star Discrepancy
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