On the randomized complexity of Banach space valued integration

• Autorzy: Stefan Heinrich , Aicke Hinrichs
• Języki publikacji: EN

Abstrakty

EN

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 nth minimal errors are bounded by $cn^{-r/d - 1 + 1/p}$ if and only if X is of equal norm type p.

Kategorie tematyczne

• 65Y20: Complexity and performance of numerical algorithms
• 65C05: Monte Carlo methods
• 65D30: Numerical integration
• 46N40: Applications in numerical analysis
• 46B07: Local theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 223
• Numer: 3
• Strony: 205-215

Daty

wydano

2014

Twórcy

autor

Stefan Heinrich

• Department of Computer Science, University of Kaiserslautern, D-67653 Kaiserslautern, Germany

autor

Aicke Hinrichs

• Institute of Analysis, Johannes Kepler University Linz, Altenberger Str. 69, A-4040 Linz, Austria

Identyfikatory

DOI

10.4064/sm223-3-2