Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights
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Publication:5101012
DOI10.1137/22M1473625MaRDI QIDQ5101012
Publication date: 2 September 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.09413
numerical integrationmedianquasi-Monte Carloweighted function spacerank-1 lattice rulehigh-order polynomial lattice rule
Monte Carlo methods (65C05) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)
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Uses Software
Cites Work
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- Quasi-Monte Carlo integration using digital nets with antithetics
- Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions
- Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
- Lattice rules with random \(n\) achieve nearly the optimal \(\mathcal{O}(n^{-\alpha-1/2})\) error independently of the dimension
- Construction of interlaced scrambled polynomial lattice rules of arbitrary high order
- Tractability of multivariate problems. Volume I: Linear information
- 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
- Lattice rules in non-periodic subspaces of Sobolev spaces
- Randomized quasi-Monte Carlo: an introduction for practitioners
- Component-by-component construction of good lattice rules with a composite number of points
- Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness
- Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
- Fast CBC construction of randomly shifted lattice rules achieving \(\mathcal{O}(n^{- 1 + \delta})\) convergence for unbounded integrands over \(\mathbb{R}^s\) in weighted spaces with POD weights
- Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces
- Proof techniques in quasi-Monte Carlo theory
- Lattice rules for nonperiodic smooth integrands
- Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules
- Jensen's inequality for medians
- Good lattice rules in weighted Korobov spaces with general weights
- Monte Carlo and quasi-Monte Carlo sampling
- Approximate formulas for some functions of prime numbers
- Component-by-component construction of good lattice rules
- Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
- Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
- Low-discrepancy point sets obtained by digital constructions over finite fields
- Primitive Polynomials Over Finite Fields
- Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation
- Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
- Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs
- On Figures of Merit for Randomly-Shifted Lattice Rules
- Polynomial Lattice Point Sets
- Introduction to Quasi-Monte Carlo Integration and Applications
- High-dimensional integration: The quasi-Monte Carlo way
- Remark on algorithm 659
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