• English
  • Deutsch
  • Log In
    or
  • Research Outputs
  • Projects
  • Researchers
  • Institutes
  • Statistics
Repository logo
Fraunhofer-Gesellschaft
  1. Home
  2. Fraunhofer-Gesellschaft
  3. Artikel
  4. On tensor product approximation of analytic functions
 
  • Details
  • Full
Options
2016
Zeitschriftenaufsatz
Titel

On tensor product approximation of analytic functions

Abstract
We prove sharp, two-sided bounds on sums of the form Sigma(d)(exp)(k epsilon N0)(Da(T))(-Sigma(d)(j=1) a(j)k(j)), where Da(T) := {k epsilon N-0(d) : Sigma(d)(j=1) a(j)k(j) <= T} and a epsilon R-+(d). These sums appear in the error analysis of tensor product approximation, interpolation and integration of d-variate analytic functions. Examples are tensor products of univariate Fourier-Legendre expansions (Beck et al., 2014) or interpolation and integration rules at Leja points (Chkifa et al., 2013), (Narayan and Jakeman, 2014), (Nobile et al., 2014). Moreover, we discuss the limit d -> infinity, where we prove both, algebraic and sub-exponential upper bounds. As an application we consider tensor products of Hardy spaces, where we study convergence rates of a certain truncated Taylor series, as well as of interpolation and integration using Leja points.
Author(s)
Griebel, M.
Oettershagen, J.
Zeitschrift
Journal of approximation theory
Thumbnail Image
DOI
10.1016/j.jat.2016.02.006
Language
Englisch
google-scholar
SCAI
  • Cookie settings
  • Imprint
  • Privacy policy
  • Api
  • Send Feedback
© 2022