A nodal spline interpolant for the Gregory rule of even order |
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Authors: | J. M. de Villiers |
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Affiliation: | (1) Department of Mathematics, University of Stellenbosch, 7600 Stellenbosch, South Africa |
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Abstract: | Summary The Gregory rule is a well-known example in numerical quadrature of a trapezoidal rule with endpoint corrections of a given order. In the literature, the methods of constructing the Gregory rule have, in contrast to Newton-Cotes quadrature,not been based on the integration of an interpolant. In this paper, after first characterizing an even-order Gregory interpolant by means of a generalized Lagrange interpolation operator, we proceed to explicitly construct such an interpolant by employing results from nodal spline interpolation, as established in recent work by the author and C.H. Rohwer. Nonoptimal order error estimates for the Gregory rule of even order are then easily obtained. |
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Keywords: | 41A55 41A15 41A05 65D32 65D30 65D07 65D05 |
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