Abstract
The asymptotic error expansion for the m N-copy quadrature rule approximation over the hypercube H N is known for some integrand functions. In this paper, we use Macsyma to investigate the outcome of applying the Levin transformation to a sequence of quadrature approximations Q (m) f, m = n + 1, n + 2, … for which these known forms of error expansion are valid. The resulting expansions suggest that in certain cases, iterated extrapolation by a low-order Levin transformation is capable of obtaining approximations more accurate than those obtained by the straightforward use of the transformation. Numerical results are presented to illustrate the effectiveness of the iterated transformation in these cases.
On leave from the University of the Philippines at Los Baños, Laguna, Philippines.
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References
R.L. Carino, I. Robinson and E. de Doncker (1990), “Approximate integration by the Levin transformation,” Technical Report 9/90, Dept. of Computer Science and Computer Engineering, La Trobe University, Australia (submitted for publication).
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MATHLAB GROUP (1977), “Macsyma Reference Manual,” Laboratory for Computer Science, MIT, Cambridge, MA.
A. Sidi (1979), “Convergence properties of some nonlinear sequence transformations,” Math. Comp., v. 33, pp.315–326.
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© 1992 Springer Science+Business Media Dordrecht
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Cariño, R., Robinson, I., de Doncker, E. (1992). An Algebraic Study of the Levin Transformation in Numerical Integration. In: Espelid, T.O., Genz, A. (eds) Numerical Integration. NATO ASI Series, vol 357. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2646-5_14
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DOI: https://doi.org/10.1007/978-94-011-2646-5_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5169-9
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