Stability analysis of algorithms for solving confluent Vandermonde-like systems
SIAM Journal on Matrix Analysis and Applications
On the construction of high-order integration formulae for the adaptive quadrature method
Journal of Computational and Applied Mathematics
Interpolatory integration formulas for optimal composition
ACM Transactions on Mathematical Software (TOMS)
Error estimation in automatic quadrature routines
ACM Transactions on Mathematical Software (TOMS)
Numerical analysis: an introduction
Numerical analysis: an introduction
A Metalgorithm for Adaptive Quadrature
Journal of the ACM (JACM)
Local Versus Global Strategies for Adaptive Quadrature
ACM Transactions on Mathematical Software (TOMS)
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
Communications of the ACM
Algorithm 379: Squank (Simpson Quadrature used adaptivity—noise killed) [D1]
Communications of the ACM
Algorithm 468: algorithm for automatic numerical integration over a finite interval [D1]
Communications of the ACM
Algorithm 303: An adaptive quadrature procedure with random panel sizes
Communications of the ACM
Algorithm 182: nonrecursive adaptive integration
Communications of the ACM
Algorithm 198: adaptive integration and multiple integration
Communications of the ACM
Algorithm 103: Simpson's rule integrator
Communications of the ACM
Algorithm 145: Adaptive numerical integration by Simpson's rule
Communications of the ACM
Computer Methods for Mathematical Computations
Computer Methods for Mathematical Computations
An adaptive extrapolation algorithm for automatic integration
ACM SIGNUM Newsletter
A comparison of some numerical integration programs
ACM SIGNUM Newsletter
Algorithm 868: Globally doubly adaptive quadrature—reliable Matlab codes
ACM Transactions on Mathematical Software (TOMS)
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
GNU Scientific Library Reference Manual - Third Edition
GNU Scientific Library Reference Manual - Third Edition
A review of error estimation in adaptive quadrature
ACM Computing Surveys (CSUR)
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We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat nonnumerical values of the integrand, how they deal with improper divergent integrals, and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in MATLAB and tested using both the “families” suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.