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Rapid computation of general interpolation formulas and mechanical quadrature rules

By Sven-Åke Gustafson

Communications of the ACM, Vol. 14 No. 12, Pages 797-801

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Let ƒ have n continuous derivatives on a closed interval [a, b] and let L be a linear functional. The attempt is made to approximate L(ƒ) with L(Q) where Q is a polynomial, approximating ƒ. Algorithms are developed for rapid computation of L(Q) for a wide class of selections of Q which includes the Lagrangian and Hermitian rules as special cases.

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