Algorithm 691: Improving QUADPACK automatic integration routines
ACM Transactions on Mathematical Software (TOMS)
Algorithm 691: Improving QUADPACK automatic integration routines
ACM Transactions on Mathematical Software (TOMS)
Local error estimates and regularity tests for the implementation of double adaptive quadrature
ACM Transactions on Mathematical Software (TOMS)
Object-oriented numerical integration: a template scheme for FEM and BEM applications
Advances in Engineering Software
Object-oriented numerical integration-a template scheme for FEM and BEM applications
Advances in Engineering Software
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
ACM Transactions on Mathematical Software (TOMS)
A review of error estimation in adaptive quadrature
ACM Computing Surveys (CSUR)
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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.