Rapid Computation of General Interpolation Formulas and Mechanical Quadrature Rules Let f have n continuous on a closed interval [a,b] and let L be a linear functional. The attempt is made to approximate L (f) with L (Q) where Q is a polynomial, approximating f. 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. CACM December, 1971 Gustafson, S. linear functionals, divided differences, Newton's interpolation formula 5.13 5.16 CA711208 JB February 2, 1978 9:49 AM 2135 4 2135 2135 4 2135 2131 5 2135 2135 5 2135 2135 5 2135 2135 5 2135 2132 5 2135 2135 6 2135 2135 6 2135