Tractability of infinite-dimensional integration in the worst case and randomized settings
From MaRDI portal
Publication:647921
DOI10.1016/j.jco.2011.01.006zbMath1230.65037OpenAlexW1980651498MaRDI QIDQ647921
Grzegorz W. Wasilkowski, Leszek Plaskota
Publication date: 21 November 2011
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jco.2011.01.006
complexityalgorithmsrandomizationreproducing kernel Hilbert spaceworst case errorpolynomial tractabilityexponent of tractabilityinfinite dimensional integration
Multidimensional problems (41A63) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20)
Related Items (32)
QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND ⋮ Countable tensor products of Hermite spaces and spaces of Gaussian kernels ⋮ MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM ⋮ Small superposition dimension and active set construction for multivariate integration under modest error demand ⋮ Liberating the Dimension for Function Approximation and Integration ⋮ Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_1\) or \(L_\infty\) ⋮ Some Results on the Complexity of Numerical Integration ⋮ Liberating the dimension for \(L_2\)-approximation ⋮ The numerical approximation of nonlinear functionals and functional differential equations ⋮ On efficient weighted integration via a change of variables ⋮ On tractability of linear tensor product problems for \(\infty \)-variate classes of functions ⋮ On weighted Hilbert spaces and integration of functions of infinitely many variables ⋮ Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces ⋮ Effective Dimension of Some Weighted Pre-Sobolev Spaces with Dominating Mixed Partial Derivatives ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ Average case tractability of approximating ∞-variate functions ⋮ Quasi-Monte Carlo and \(\varepsilon\)-truncation dimension in ANOVA spaces ⋮ The cost of deterministic, adaptive, automatic algorithms: cones, not balls ⋮ Infinite-dimensional integration and the multivariate decomposition method ⋮ Liberating the dimension for function approximation: standard information ⋮ Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition ⋮ Embeddings for infinite-dimensional integration and \(L_2\)-approximation with increasing smoothness ⋮ Efficient Implementations of the Multivariate Decomposition Method for Approximating Infinite-Variate Integrals ⋮ Hyperbolic cross approximation in infinite dimensions ⋮ Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration ⋮ MDFEM: multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM ⋮ \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems ⋮ Infinite-dimensional integration on weighted Hilbert spaces ⋮ Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Deterministic multi-level algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
- Liberating the dimension for function approximation: standard information
- Liberating the dimension
- Average case optimality for linear problems
- Infinite-dimensional quadrature and approximation of distributions
- Tractability of multivariate problems. Volume I: Linear information
- Optimal importance sampling for the approximation of integrals
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- Multi-level Monte Carlo algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
- Deterministic and stochastic error bounds in numerical analysis
- Explicit cost bounds of algorithms for multivariate tensor product problems
- Average-case analysis of numerical problems
- Infinite-dimensional integration on weighted Hilbert spaces
- The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
- Monte Carlo Simulation of Stochastic Integrals when the Cost of Function Evaluation Is Dimension Dependent
- The power of standard information for multivariate approximation in the randomized setting
- On decompositions of multivariate functions
- On tractability of path integration
- Liberating the Dimension for Function Approximation and Integration
- A new algorithm and worst case complexity for Feynman-Kac path integration.
This page was built for publication: Tractability of infinite-dimensional integration in the worst case and randomized settings
