Liberating the dimension for L2-approximation

G. W. Wasilkowski

doi:10.1016/j.jco.2011.12.002

Liberating the dimension for L₂-approximation

G. W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We consider approximation of ∞-variate functions with the error measured in a weighted L₂-norm. The functions being approximated belong to weighted tensor product spaces with arbitrary weights γ_μ. We provide complexity upper bounds and sufficient conditions for polynomial and weak tractabilities expressed in terms of the properties of the weights γ_μ and the complexity of the corresponding univariate approximation problem. These tractability conditions are also necessary for important types of weights including product weights.

Original language	English
Pages (from-to)	304-319
Number of pages	16
Journal	Journal of Complexity
Volume	28
Issue number	3
DOIs	https://doi.org/10.1016/j.jco.2011.12.002
State	Published - Jun 2012

Keywords

Approximation
Complexity
Integration
Tractability

ASJC Scopus subject areas

Algebra and Number Theory
Statistics and Probability
Numerical Analysis
General Mathematics
Control and Optimization
Applied Mathematics

Access to Document

10.1016/j.jco.2011.12.002

Cite this

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