An Adaptive Algorithm for the
Approximate Calculation of
Multiple Integrals

Jarle Berntsen and Terje O. Espelid
Department of Informatics
University of Bergen
Allegt. 55, N-5000 Bergen
Norway
- Alan Genz
Mathematics Department
Washington State University
Pullman, WA 99164-3113
U. S. A.

Abstract:

An adaptive algorithm for numerical integration over hyperrectangular regions is described. The algorithm uses a globally adaptive subdivision strategy. Several precautions are introduced in the error estimation in order to improve the reliability. In each dimension more than one integration rule is made available to the user. The algorithm has been structured to allow efficient implementation on shared memory parallel computers.
Keywords: automatic integration, adaptive, cubature, multidimensional integration, fully symmetric rules, null rules, parallel algorithms.

 
• Introduction
• The Globally Adaptive Algorithm
• Integration Rules and Null Rules
• Error Estimation
• Testing
• Concluding Remarks
• Acknowledgements
• References