Istituto di Scienza e Tecnologie dell'Informazione     
Favati P., Lotti G., Romani F. Interpolatory integration formulas for optimal composition. Internal note IEI-B4-15, 1987.
A set of symmetric, closed, interpolatory integration formu1as on the interval [-1, 1] is investigated. These formulas, called recursive monotone, have the property that higher order or compound rules can be applied without wasting previous computed functional values. An exhaustive search shows the existence of 27 families of recursive monotone formulas with positive weights and increasing degree of precision, stemming from the simple trapezoidal rule. The numerical behaviour of the formulas is experimented.

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