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Remainders in Interpolation and Quadrature Formulae

Published online by Cambridge University Press:  03 November 2016

P. J. Daniell
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Extract

The determination of the errors involved in interpolation or quadrature formulae often involves complicated reasoning. There are many cases, however, where the remainder can be obtained very easily. These cases belong to the class which we call simplex.

In general a formula will be expressible in the form

L(f) =∑rArf(xr) + ∑sBsf'(xs)+ ∑tCtf''(xt) +… ......(1)

to a finite number of terms and it is assumed throughout that f(x) possesses derivatives as far as the remainder may require.

Type
Research Article
Information
The Mathematical Gazette , Volume 24 , Issue 261 , October 1940 , pp. 238 - 244
Copyright
Copyright © Mathematical Association 1940

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References

* L. M. Milne-Thomson, Calculus of Finite Differences, p. 160.

* J. C. Adams, Collected Scientific Paper I, p. 464.