D01 (Quad) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
d01ahf
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One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands
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One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands
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d01alf
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d01anf
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One-dimensional quadrature, adaptive, finite interval, weight function $\mathrm{cos}\left(\omega x\right)$ or $\mathrm{sin}\left(\omega x\right)$
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One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type
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One-dimensional quadrature, adaptive, finite interval, weight function $1/\left(x-c\right)$, Cauchy principal value (Hilbert transform)
d01arf
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One-dimensional quadrature, adaptive, semi-infinite interval, weight function $\mathrm{cos}\left(\omega x\right)$ or $\mathrm{sin}\left(\omega x\right)$
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One-dimensional quadrature, adaptive, finite interval, variant of d01ajf efficient on vector machines
d01auf
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One-dimensional quadrature, adaptive, finite interval, variant of d01akf efficient on vector machines
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Example Plot
Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule
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Example Plot
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Multidimensional quadrature, Sag–Szekeres method, general product region or $n$-sphere
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Example Data
One-dimensional quadrature, integration of function defined by data values, Gill–Miller method
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Multidimensional quadrature over hyper-rectangle, Monte Carlo method
d01gcf
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Multidimensional quadrature, general product region, number-theoretic method
d01gdf
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Multidimensional quadrature, general product region, number-theoretic method, variant of d01gcf efficient on vector machines
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Korobov optimal coefficients for use in d01gcf or d01gdf, when number of points is prime
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Korobov optimal coefficients for use in d01gcf or d01gdf, when number of points is product of two primes
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Multidimensional quadrature over an $n$-sphere, allowing for badly behaved integrands
d01paf
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Multidimensional quadrature over an $n$-simplex
d01raf
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Diagnostic routine for d01raf
Determine required array dimensions for d01raf
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Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule
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Calculation of weights and abscissae for Gaussian quadrature rules, method of Golub and Welsch
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