Infinite-dimensional integration on weighted Hilbert spaces
From MaRDI portal
Publication:2840006
DOI10.1090/S0025-5718-2012-02583-XzbMath1284.65044MaRDI QIDQ2840006
Publication date: 17 July 2013
Published in: Mathematics of Computation (Search for Journal in Brave)
algorithmreproducing kernel Hilbert spaceweighted Hilbert spacesinfinite-dimensional integration\(L_{2}\)-star discrepancypolynomially tractableworst case \(\epsilon\)-complexity
Monte Carlo methods (65C05) 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) Irregularities of distribution, discrepancy (11K38)
Related Items (20)
Liberating the Dimension for Function Approximation and Integration ⋮ Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ Some Results on the Complexity of Numerical Integration ⋮ The average values of a kind of functionals in LP and concentration without measure ⋮ Liberating the dimension for \(L_2\)-approximation ⋮ 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 ⋮ Tractability of infinite-dimensional integration in the worst case and randomized settings ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ Average case tractability of approximating ∞-variate functions ⋮ Deterministic multi-level algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\) ⋮ 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 ⋮ Hyperbolic cross approximation in infinite dimensions ⋮ Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration ⋮ 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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Deterministic multi-level algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
- Tractability of infinite-dimensional integration in the worst case and randomized settings
- Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces
- Liberating the dimension
- Algorithmic construction of low-discrepancy point sets via dependent randomized rounding
- On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
- Infinite-dimensional quadrature and approximation of distributions
- Generalized tractability for multivariate problems. I: Linear tensor product problems and linear information
- Tractability of multivariate problems. Volume I: Linear information
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- Multi-level Monte Carlo algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
- Low-discrepancy and low-dispersion sequences
- When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
- Monte Carlo complexity of global solution of integral equations
- Low-discrepancy sequences and global function fields with many rational places
- Finite-order weights imply tractability of multivariate integration
- Liberating the weights
- Good lattice rules in weighted Korobov spaces with general weights
- The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
- Multilevel Monte Carlo Path Simulation
- Variable Subspace Sampling and Multi-level Algorithms
- Monte Carlo Simulation of Stochastic Integrals when the Cost of Function Evaluation Is Dimension Dependent
- On decompositions of multivariate functions
- Discrépance de suites associées à un système de numération (en dimension s)
- A generalized discrepancy and quadrature error bound
- On tractability of path integration
- Theory of Reproducing Kernels
- A new algorithm and worst case complexity for Feynman-Kac path integration.
This page was built for publication: Infinite-dimensional integration on weighted Hilbert spaces
