Karl Deckers
Abstract
We present a numerical procedure to approximate integrals of the form ∫baf(x)dx, where f is a function with singularities close to, but outside the interval [a, b], with − ∞ ⩽ a < b ⩽ +∞. The algorithm is based on rational interpolatory Fejér quadrature rules, together with a sequence of real and/or complex conjugate poles that are given in advance. Since for n fixed in advance, the accuracy of the computed nodes and weights in the n-point rational quadrature formula strongly depends on the given sequence of poles, we propose a small number of iterations over the number of points in the rational quadrature rule, limited by the value n (instead of fixing the number of points in advance) in order to obtain the best approximation among the first n.
The proposed algorithm is implemented as a Matlab program.
Supplemental Material
Available for Download
Software for Extended Rational Fejér Quadrature Rules Based on Chebyshev Orthogonal Rational Functions
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Index Terms
- Algorithm 973: Extended Rational Fejér Quadrature Rules Based on Chebyshev Orthogonal Rational Functions
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