Cubature rules of prescribed merit

Technical Report · Fri Mar 01 00:00:00 EST 1996

DOI:https://doi.org/10.2172/211665· OSTI ID:211665

Lyness, J N ^[1]; Sloan, I H ^[2]

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1. Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
2. New South Wales Univ., Sydney, NSW (Australia). School of Mathematics

We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for the hypercube: this is the merit of a rule, which is closely related to its trigonometric degree, and which reduces to the Zaremba figure of merit in the case of a lattice rule. We derive a family of rules Q{sub k}{sup a} having dimension s and merit 2{sup k}. These rules seem to be competitive with lattice rules with respect to the merit that can be achieved with a given number of abscissas.

• Research Organization: Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
• Sponsoring Organization: USDOE, Washington, DC (United States); Australian Research Council, Canberra, ACT (Australia)
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 211665
• Report Number(s): MCS-P437-0594; ON: DE96007616
• Resource Relation: Other Information: PBD: [1996]
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
HYPERCUBE COMPUTERS
ALGORITHMS
COMPUTER CALCULATIONS
CALCULATION METHODS
MATHEMATICAL MODELS
RECURSION RELATIONS
WEIGHTING FUNCTIONS