The EulerMaclaurin expansion for the simplex
Authors:
J. N. Lyness and K. K. Puri
Journal:
Math. Comp. 27 (1973), 273293
MSC:
Primary 65D30
MathSciNet review:
0375752
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Abstract: A natural extension of the onedimensional trapezoidal rule to the simplex , is a rule Rf which uses as abscissas all those points on a hyperrectangular lattice of spacing which lie within the simplex, assigning an equal weight to each interior point. In this paper, rules of this type are defined and some of their properties are derived. In particular, it is shown that the error functional satisfies an EulerMaclaurin expansion of the type so long as and its partial derivatives of order up to p are continuous. Conditions under which this asymptotic series terminates are given, together with the condition for odd terms to drop out leaving an even expansion. The application to Romberg integration is discussed.
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 I. Navot, "A further extension of the EulerMaclaurin summation formula," J. Math. and Phys., v. 41, 1962, pp. 155163.
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DOI:
http://dx.doi.org/10.1090/S00255718197303757521
PII:
S 00255718(1973)03757521
Article copyright:
© Copyright 1973
American Mathematical Society
