Using the Multivariate Decomposition Method (MDM), we develop an efficient algorithm for approximating the8-variate integralfor a class of functions f that are once differentiable with respect to each variable.MDM requires efficient algorithms for d-variate versions of the problem. Such algorithms are provided by Smolyaks construction which is based on efficient algorithms for the univariate integrationDetailed analysis and development of (nearly) optimal quadratures for I (f) is the main contribution of the current paper.
|Number of pages||19|
|State||Published - Sep 25 2014|
Bibliographical notePublisher Copyright:
© 2013, Springer Science+BusinessMedia New York.
- Multivariate integration
- Weighted integrals
- Weighted trapezoid rules
- ∞-Variate functions
ASJC Scopus subject areas
- Applied Mathematics