Summary: Evolutionary Bioinformatics Online 2006: 2 261269 261
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Gaussian Quadrature Formulae
for Arbitrary Positive Measures
Andrew D. Fernandes1,2
and William R. Atchley1,2,3
Graduate Program in Biomathematics. 2
Center for Computational Biology. 3
Department of Genetics,
North Carolina State University Raleigh, NC 27695-7614.
Abstract: We present computational methods and subroutines to compute Gaussian quadrature integration formulas for
arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature
schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general
ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-
gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme.
Availability: Source code is freely available online as a C-linkable ISO C++ library under a BSD-style license from
http://www.fernandes.org/gaussqr. The library may be built using single, double, or extended precision arithmetic.