Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure

DOI10.1090/S0273-0979-1993-00379-3zbMath0770.41020arXivmath/9304216OpenAlexW1978072899MaRDI QIDQ4695332

Grzegorz W. Wasilkowski

Publication date: 21 July 1993

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9304216

zbMATH Keywords

multivariate integrationisotropic Wiener measure

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Multidimensional problems (41A63) Algorithms for approximation of functions (65D15) Approximate quadratures (41A55) Numerical integration (65D30)

Related Items (10)

Optimal designs for weighted approximation and integration of stochastic processes on \([0,\infty)\) ⋮ Scrambled net variance for integrals of smooth functions ⋮ A survey of average case complexity for linear multivariate problems ⋮ Multivariate \(L_{\infty}\) approximation in the worst case setting over reproducing kernel Hilbert spaces ⋮ Average case complexity of linear multivariate problems. I: Theory ⋮ On the exponent of discrepancies ⋮ On the optimal convergence rate of universal and nonuniversal algorithms for multivariate integration and approximation ⋮ New averaging technique for approximating weighted integrals ⋮ Average case complexity of linear multivariate problems ⋮ The asymptotic efficiency of randomized nets for quadrature

Cites Work

• Can adaption help on the average?
• Approximation of linear functionals on a Banach space with a Gaussian measure
• Randomization for continuous problems
• Average case complexity of linear multivariate problems. II: Applications
• Deterministic and stochastic error bounds in numerical analysis
• Information of varying cardinality
• Approximation of linear operators on a Wiener space
• Approximation and optimization on the Wiener space
• Average case complexity of multivariate integration
• On the Power of Adaptive Information for Functions with Singularities
• A Modified Monte-Carlo Quadrature
• On Some Problems Concerning Brownian Motion in Lévy’s Sense
• A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
• On the Regression Design Problem of Sacks and Ylvisaker
• Designs for Regression Problems with Correlated Errors III
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