Symmetric integration rules for hypercubes. I. Error coefficients
Author:
J. N. Lyness
Journal:
Math. Comp. 19 (1965), 260276
MSC:
Primary 65.55
MathSciNet review:
0201067
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Abstract: A compact notation is introduced to describe and systematise symmetric integration rules and the EulerMaclaurin expansion is used to describe their error terms. The application to cytolic rules is discussed especially in relation to the number of function evaluations required. This paper is devoted exclusively to theory, illustrated by wellknown results. This theory leads to new powerful integration rules which will be published shortly.
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 P. C. Hammer & A. H. Stroud, "Numerical evaluation of multiple integrals. II," MTAC, v. 12, 1958, pp. 272280. MR 21 #970. MR 0102176 (21:970)
 [2]
 J. N. Lyness & J. B. B. McHugh, "A progressive procedure," Comput. J., v. 6, 1963/64, pp. 264270.
 [3]
 J. C. P. Miller, "Numerical quadrature over a rectangular domain in two or more dimensions. I: Quadrature over a square, using up to sixteen equally spaced points," Math. Comp., v. 14, 1960, pp. 1320. MR 22 #1075. MR 0110193 (22:1075)
 [4]
 J. C. P. Miller, "Numerical quadrature over a rectangular domain in two or more dimensions. II: Quadrature in several dimensions, using special points," Math. Comp., v. 14, 1960, pp. 130138. MR 22 #6075. MR 0115273 (22:6075)
 [5]
 D. Mustard, J. N. Lyness & J. M. Blatt, "Numerical quadrature in dimensions," Comput. J., v. 6, 1963/64, pp. 7587. MR 28 #1762. MR 0158539 (28:1762)
 [6]
 D. Mustard, "Approximate integration in dimensions," Thesis, Univ. of New South Wales, Australia, 1964.
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 M. Sadowsky, "A formula for approximate computation of a triple integral," Amer. Math. Monthly, v. 47, 1940, pp. 539543. MR 2, 62. MR 0002496 (2:62k)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196502010673
PII:
S 00255718(1965)02010673
Article copyright:
© Copyright 1965
American Mathematical Society
