Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
From MaRDI portal
Publication:3631927
DOI10.1137/060666639zbMath1189.42012arXiv1304.0328OpenAlexW2014551121MaRDI QIDQ3631927
Publication date: 22 June 2009
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1304.0328
Monte Carlo methods (65C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)
Related Items
On tensor product approximation of analytic functions ⋮ Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs? ⋮ Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions ⋮ Higher-Order Quasi-Monte Carlo for Bayesian Shape Inversion ⋮ QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach ⋮ Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\) ⋮ Quasi-Monte Carlo point sets with small \(t\)-values and WAFOM ⋮ A search for extensible low-WAFOM point sets ⋮ Existence of Higher Order Convergent Quasi-Monte Carlo Rules via Walsh Figure of Merit ⋮ ANOVA Decomposition of Convex Piecewise Linear Functions ⋮ BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension ⋮ Construction of interlaced polynomial lattice rules for infinitely differentiable functions ⋮ Approximation of quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions ⋮ Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences ⋮ Construction of interlaced scrambled polynomial lattice rules of arbitrary high order ⋮ Point sets with optimal order of extreme and periodic discrepancy ⋮ Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights ⋮ Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC ⋮ Computational Higher Order Quasi-Monte Carlo Integration ⋮ The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets ⋮ From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules ⋮ Duality theory and propagation rules for higher order nets ⋮ Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere ⋮ A Tool for Custom Construction of QMC and RQMC Point Sets ⋮ On Dropping the First Sobol’ Point ⋮ A Universal Median Quasi-Monte Carlo Integration ⋮ DISCREPANCY OF SECOND ORDER DIGITAL SEQUENCES IN FUNCTION SPACES WITH DOMINATING MIXED SMOOTHNESS ⋮ Discrepancy of Digital Sequences: New Results on a Classical QMC Topic ⋮ Higher order quasi-Monte Carlo integration for Bayesian PDE inversion ⋮ Optimal periodic \(L_2\)-discrepancy and diaphony bounds for higher order digital sequences ⋮ Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands ⋮ Lattice rules for nonperiodic smooth integrands ⋮ An explicit construction of point sets with large minimum Dick weight ⋮ Lattice rules in non-periodic subspaces of Sobolev spaces ⋮ Sparse Compression of Expected Solution Operators ⋮ Multilevel higher-order quasi-Monte Carlo Bayesian estimation ⋮ Koksma-Hlawka type inequalities of fractional order ⋮ On the \(L_p\) discrepancy of two-dimensional folded Hammersley point sets ⋮ Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules ⋮ Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness ⋮ Cubature Formulas for Multisymmetric Functions and Applications to Stochastic Partial Differential Equations ⋮ Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules ⋮ On the existence of higher order polynomial lattices based on a generalized figure of merit ⋮ A computable figure of merit for quasi-Monte Carlo point sets ⋮ A quasi-Monte Carlo data compression algorithm for machine learning ⋮ Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation ⋮ Richardson Extrapolation of Polynomial Lattice Rules ⋮ Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions ⋮ Optimal order quadrature error bounds for infinite-dimensional higher-order digital sequences ⋮ 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 ⋮ A higher order Blokh-Zyablov propagation rule for higher order nets ⋮ Constructing good higher order polynomial lattice rules with modulus of reduced degree ⋮ Quasi-Monte Carlo methods with applications in finance ⋮ Construction algorithms for higher order polynomial lattice rules ⋮ Duality theory and propagation rules for generalized digital nets ⋮ The smoothing effect of the ANOVA decomposition ⋮ Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration ⋮ Convergence analysis of deterministic kernel-based quadrature rules in misspecified settings ⋮ Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations ⋮ An Explicit Construction of Optimal Order Quasi--Monte Carlo Rules for Smooth Integrands ⋮ Calibration of financial models using quasi-Monte Carlo ⋮ Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification ⋮ THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS ⋮ Lp- and Sp,qrB-discrepancy of (order 2) digital nets ⋮ On the approximation of smooth functions using generalized digital nets ⋮ A High Performance Computing and Sensitivity Analysis Algorithm for Stochastic Many-Particle Wave Scattering ⋮ The \(b\)-adic tent transformation for quasi-Monte Carlo integration using digital nets ⋮ Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration ⋮ Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets ⋮ Quasi-Monte Carlo methods for linear two-stage stochastic programming problems ⋮ Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces ⋮ Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients