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1977•IMA Journal of Applied MathematicsRequires access

An Alternative Strategy for Cautions Adaptive Quadrature

L. J. Hazlewood

Open publisher page 2 citations

Abstract

An algorithm for adaptive quadrature is presented which attempts to ensure that the quadrature used is valid for the behaviour of the integrand. This is achieved by using another algorithm to examine the finite differences of the integrand. The order of the quadrature and the interval subdivision strategy used form an integral part of this algorithm. The resulting adaptive quadrature algorithm is very reliable while its efficiency appears to be of the order of other adaptive quadrature algorithms in the literature.

About this research paper

What this paper is about

An algorithm for adaptive quadrature is presented which attempts to ensure that the quadrature used is valid for the behaviour of the integrand. This is achieved by using another algorithm to examine the finite differences of the integrand. The order of the quadrature and the interval subdivision strategy used form an integral part of this algorithm. The resulting adaptive quadrature algorithm is very reliable while its efficiency appears to be of the order of other adaptive quadrature algorithms in the literature.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

An algorithm for adaptive quadrature is presented which attempts to ensure that the quadrature used is valid for the behaviour of the integrand. This is achieved by using another algorithm to examine the finite differences of the integrand. The order of the quadrature and the interval subdivision strategy used form an integral part of this algorithm. The resulting adaptive quadrature algorithm is very reliable while its efficiency appears to be of the order of other adaptive quadrature algorithms in the literature.

Key concepts: Adaptive quadrature, Clenshaw–Curtis quadrature, Tanh-sinh quadrature, Quadrature (astronomy), Gauss–Kronrod quadrature formula, Gauss–Laguerre quadrature, Gauss–Hermite quadrature, Gauss–Jacobi quadrature

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