Cubature formulas of degree nine for symmetric planar regions
Authors:
Robert Piessens and Ann Haegemans
Journal:
Math. Comp. 29 (1975), 810815
MSC:
Primary 65D30
MathSciNet review:
0368393
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Abstract: A method of constructing 19point cubature formulas with degree of exactness 9 is given for twodimensional regions and weight functions which are symmetric in each variable. For some regions, e.g., the square and the circle, these formulas can be reduced to 18point formulas.
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A. HAEGEMANS & R. PIESSENS, Tables of Cubature Formulas of Degree Nine for Symmetric Planar Regions. (Report to be published.)
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 P. RABINOWITZ & N. RICHTER, "Perfectly symmetric twodimensional integration formulas with minimal number of points," Math. Comp., v. 23, 1969, pp. 765779. MR 41 #2928. MR 0258281 (41:2928)
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 A. H. STROUD, Approximate Calculation of Multiple Integrals, PrenticeHall Ser. in Automatic Computation, PrenticeHall, Englewood Cliffs, N. J., 1971. MR 48 #5348. MR 0327006 (48:5348)
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 A. HAEGEMANS & R. PIESSENS, Tables of Cubature Formulas of Degree Nine for Symmetric Planar Regions. (Report to be published.)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197503683935
PII:
S 00255718(1975)03683935
Keywords:
Approximate integration,
cubature formula,
degree of exactness,
planar region,
orthogonal polynomials
Article copyright:
© Copyright 1975
American Mathematical Society
