On Tractability of Weighted Integration for Certain Banach Spaces of Functions

Fred J. Hickernell (), Ian H. Sloan () and Grzegorz W. Wasilkowski ()
Additional contact information
Fred J. Hickernell: Hong Kong Baptist University, Department of Mathematics
Ian H. Sloan: School of Mathematics
Grzegorz W. Wasilkowski: University of Kentucky, Department of Computer Science

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2002, 2004, pp 51-71 from Springer

Abstract: Summary There are a number of results on tractability and strong tractability for the integration problem over bounded domains. However, the majority of them assume functions with dominating mixed partial derivatives bounded in the L 2 norm. Much less is known when the derivatives are bounded in the L 1 norm, and almost nothing when a finite L p norm is assumed for an arbitrary p. The focus of this paper is to extend known tractability results to weighted spaces of functions with the derivatives bounded in L p norms and the norms of the derivatives then combined via weighted L q norms. Moreover, we consider weighted integration with the domain of integration being not necessarily bounded. It turns out that tractability and strong tractability depend only on q for bounded D, whereas they depend on both parameters p and q for unbounded D.

Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18743-8_3

Ordering information: This item can be ordered from
http://www.springer.com/9783642187438

DOI: 10.1007/978-3-642-18743-8_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().