Istituto di Scienza e Tecnologie dell'Informazione     
Favati P., Lotti G., Romani F. Interpolatory integration formulas for optimal composition. In: ACM Transactions on Mathematical Software, vol. 17 (2) pp. 207 - 217. ACM, 1991.
A set of symmetric, closed, interpolatory integration formulas on the interval [-1, 1] with positive weights and increasing degree of precision is introduced. These formulas, called recursive monotone stable (RMS) formulas, allow applying higher order or compound rules without wasting previously computed functional values. An exhaustive search shows the existence of 27 families of RMS formulas, stemming from the simple trapezoidal rule.
Subject Algorithms
Interpolatory quadrature
Program testing
G.1.4 Quadrature and Numerical Differentiation. Adaptive and iterative quadrature
G.4 Mathematical Software. Algorithm design and analysis

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