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Topic: Trapezoidal rule

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Numerical integration

Trapezium

Uys Krige

	Integral - Wikipedia, the free encyclopedia
		One popular method, called the rectangle method, relies on dividing the region under the function into a series of rectangles and finding the sum.
		Other well-known methods are the trapezoidal rule and Simpson's rule.
		Some integrals cannot be found exactly, and others are so complex that finding the exact answer would be extremely time-consuming or computationally intensive.
	en.wikipedia.org /wiki/Integral (1744 words)

	1994 Abstracts of MCS Reports and Preprints
		The context of this note is the discretization error made by the m-panel trapezoidal rule when the integrand has an algebraic singularity at one end, say x = 0, of the finite integration interval.
		This paper introduces a criterion for the evaluation of multidimensional quadrature, or cubature, rules for the hypercube: this is the {\it 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.
		These rules seem to be competitive with lattice rules with respect to the merit that can be achieved with a given number of abscissas.
	www-fp.mcs.anl.gov /division/publications/abstracts/abstracts94.htm (9663 words)

	Publications of the SPACES team
		Our first contribution is a generic algorithm which enables one to describe all the known algorithms based on Descartes' rule of sign and the bissection strategy in a unified framework.
		Using that framework, a new algorithm is presented, which is optimal in terms of memory usage and as fast as both Collins and Akritas' algorithm and Krandick variant, independently of the input polynomial.
		In the case where none of the masses are on the axis (trapezoidal configuration), it is rather easy to show that for any value of the two masses, there is exactly one central configuration.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	Bibliography
		Allasia and R. Besenghi, Numerical calculation of incomplete gamma functions by the trapezoidal rule, Numer.
		Allasia and R. Besenghi, Numerical calculation of the Riemann zeta function and generalizations by means of the trapezoidal rule, Numerical and Applied Mathematics, Part 2 (Paris 1988) (C. Brezinski, ed.), IMACS Ann.
		Allasia and R. Besenghi, Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule, Rend.
	math.nist.gov /mcsd/Reports/2001/nesf/node38.html (8398 words)

	Integral Article, Integral Information (Site not responding. Last check: 2007-11-01)
		Definite integrals may be approximated using several methods.
		One popular method, called the rectangle method or the trapezoidal rule, relies on dividing the function into a series ofrectangles and finding the sum.
		Some integrals cannot be found exactly, and others are so complex that finding the exact answer would be extremelytime-consuming or computationally-intensive.
	www.anoca.org /integrals/integration/integral.html (1330 words)

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