Liberating the dimension for function approximation

DOI10.1016/j.jco.2010.08.004zbMath1208.65024OpenAlexW2011665537MaRDI QIDQ617660

Henryk Woźniakowski, Grzegorz W. Wasilkowski

Publication date: 21 January 2011

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2010.08.004

zbMATH Keywords

complexitymultivariate function approximationtractabilityoptimal algorithmsinfinitely many variables

Mathematics Subject Classification ID

Algorithms for approximation of functions (65D15)

Related Items (16)

Stable splittings of Hilbert spaces of functions of infinitely many variables ⋮ Liberating the Dimension for Function Approximation and Integration ⋮ Grouped Transformations and Regularization in High-Dimensional Explainable ANOVA Approximation ⋮ 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 ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ Effective Dimension of Some Weighted Pre-Sobolev Spaces with Dominating Mixed Partial Derivatives ⋮ Average case tractability of approximating ∞-variate functions ⋮ 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 ⋮ Hyperbolic cross approximation in infinite dimensions ⋮ \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems

Cites Work

• Liberating the dimension
• On the tractability of linear tensor product problems in the worst case
• 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.
• Monte Carlo Simulation of Stochastic Integrals when the Cost of Function Evaluation Is Dimension Dependent
• On tractability of path integration
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