Generalized tractability for multivariate problems. I: Linear tensor product problems and linear information

DOI10.1016/j.jco.2006.06.006zbMath1118.65001OpenAlexW1980001337MaRDI QIDQ883336

Michael Gnewuch, Henryk Woźniakowski

Publication date: 4 June 2007

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

Full work available at URL: https://doi.org/10.1016/j.jco.2006.06.006

zbMATH Keywords

Information-based complexityEigenvaluesMultivariate problemWorst-case error

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Monte Carlo methods (65C05) Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30)

Related Items

Generalized tractability for multivariate problems. II: Linear tensor product problems, linear information, and unrestricted tractability, Multivariate approximation for analytic functions with Gaussian kernels, Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence, Quasi-polynomial tractability of linear problems in the average case setting, Quasi-polynomial tractability, Liberating the dimension, Breaking the curse of dimensionality, Infinite-dimensional integration on weighted Hilbert spaces

Cites Work

• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability and strong tractability of linear multivariate problems
• Quasi-Monte Carlo methods can be efficient for integration over products of spheres
• Finite-order weights imply tractability of linear multivariate problems
• Worst case complexity of multivariate Feynman--Kac path integration
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