Average case tractability of approximating ∞-variate functions
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Publication:5401703
DOI10.1090/S0025-5718-2013-02759-7zbMath1301.41026MaRDI QIDQ5401703
Publication date: 12 March 2014
Published in: Mathematics of Computation (Search for Journal in Brave)
Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)
Related Items (7)
Some Results on the Complexity of Numerical Integration ⋮ On tractability of linear tensor product problems for \(\infty \)-variate classes of functions ⋮ Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ The cost of deterministic, adaptive, automatic algorithms: cones, not balls ⋮ Infinite-dimensional integration and the multivariate decomposition method ⋮ \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems
Cites Work
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- Liberating the dimension for \(L_2\)-approximation
- Deterministic multi-level algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
- Liberating the dimension for function approximation: standard information
- Liberating the dimension for function approximation
- Tractability of infinite-dimensional integration in the worst case and randomized settings
- Liberating the dimension
- On the average complexity of multivariate problems
- Infinite-dimensional quadrature and approximation of distributions
- 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 \(\mathbb R^{\mathbb N}\)
- Average case optimal algorithms in Hilbert spaces
- Optimal algorithms for linear problems with Gaussian measures
- Information of varying cardinality
- Integration and approximation in arbitrary dimensions
- Infinite-dimensional integration on weighted Hilbert spaces
- Monte Carlo Simulation of Stochastic Integrals when the Cost of Function Evaluation Is Dimension Dependent
- On decompositions of multivariate functions
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
- On tractability of path integration
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
- A new algorithm and worst case complexity for Feynman-Kac path integration.
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