Authors

Citation

J. Berntsen et al., ALGORITHM 720 - AN ALGORITHM FOR ADAPTIVE CUBATURE OVER A COLLECTION OF 3-DIMENSIONAL SIMPLICES, ACM transactions on mathematical software, 19(3), 1993, pp. 320-332

Citations number

17

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Computer Sciences",Mathematics

Journal title

ISSN journal

0098-3500

Volume

19

Issue

3

Year of publication

1993

Pages

320 - 332

Database

ISI

SICI code

0098-3500(1993)19:3<320:A7-AAF>2.0.ZU;2-I

Abstract

An adaptive algorithm for computing an approximation to the integral o
f each element in a vector of functions over a 3-dimensional region co
vered by simplices is presented. The algorithm is encoded in FORTRAN 7
7. Locally, a cubature formula of degree 8 with 43 points is used to a
pproximate an integral. The local error estimate is based on the same
evaluation points. The error estimation procedure tries to decide whet
her the approximation for each function has asymptotic behavior, and d
ifferent actions are taken depending on that decision. The simplex wit
h the largest error is subdivided into 8 simplices. The local procedur
e is then applied to each new region. This procedure is repeated until
convergence,