Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quadrature formulas for monotone functions


Author: Erich Novak
Journal: Proc. Amer. Math. Soc. 115 (1992), 59-68
MSC: Primary 41A55; Secondary 65C05, 65D32
MathSciNet review: 1086337
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that adaptive quadrature formulas for the class of monotone functions are much better than nonadaptive ones if the average error is considered. Up to now it was only known that adaptive methods are not better in the worst case (for this and many other classes of functions) or in various average case settings.

We also prove that adaptive Monte Carlo methods are much better than nonadaptive ones. This also contrasts with analogous results for other classes (Sobolev classes, Hölder classes) where adaptive methods are only slightly better than nonadaptive ones.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A55, 65C05, 65D32

Retrieve articles in all journals with MSC: 41A55, 65C05, 65D32


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1086337-X
PII: S 0002-9939(1992)1086337-X
Article copyright: © Copyright 1992 American Mathematical Society