Smolyak's construction of cubature formulas of arbitrary trigonometric degree

Authors
Cools, R Novak, E Ritter, K
Citation
R. Cools et al., Smolyak's construction of cubature formulas of arbitrary trigonometric degree, COMPUTING, 62(2), 1999, pp. 147-162
Citations number
21
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTING
ISSN journal
0010485X → ACNP
Volume
62
Issue
2
Year of publication
1999
Pages
147 - 162
Database
ISI
SICI code
0010-485X(1999)62:2<147:SCOCFO>2.0.ZU;2-C
Abstract
We study cubature formulas for d-dimensional integrals with a high trigonom etric degree. To obtain a trigonometric degree l in dimension d, we need ab out d(l)/l! function values if d is large. Only a small number of arithmeti cal operations is needed to construct the cubature formulas using Smolyak's technique. We also compare different methods to obtain formulas with high trigonometric degree.