A+ CATEGORY SCIENTIFIC UNIT

On the randomized complexity of Banach space valued integration

Volume 223 / 2014

Stefan Heinrich, Aicke Hinrichs Studia Mathematica 223 (2014), 205-215 MSC: Primary 65D30; Secondary 46B07, 46N40, 65C05, 65Y20. DOI: 10.4064/sm223-3-2

Abstract

We study the complexity of Banach space valued integration in the randomized setting. We are concerned with $r$ times continuously differentiable functions on the $d$-dimensional unit cube $Q$, with values in a Banach space $X$, and investigate the relation of the optimal convergence rate to the geometry of $X$. It turns out that the $n$th minimal errors are bounded by $cn^{-r/d-1+1/p}$ if and only if $X$ is of equal norm type $p$.

Authors

  • Stefan HeinrichDepartment of Computer Science
    University of Kaiserslautern
    D-67653 Kaiserslautern, Germany
    e-mail
  • Aicke HinrichsInstitute of Analysis
    Johannes Kepler University Linz
    Altenberger Str. 69
    A-4040 Linz, Austria
    e-mail

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