Gaussian Quadrature Formulae for Arbitrary Positive Measures

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 numeri...

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Detalles Bibliográficos
Autores principales: Fernandes, Andrew D., Atchley, William R.
Formato: Texto
Lenguaje:English
Publicado: Libertas Academica 2007
Materias:
Original Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2674649/
https://www.ncbi.nlm.nih.gov/pubmed/19455218
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author Fernandes, Andrew D.
Atchley, William R.
author_facet Fernandes, Andrew D.
Atchley, William R.
author_sort Fernandes, Andrew D.
collection PubMed
description 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.
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spelling pubmed-26746492009-05-19 Gaussian Quadrature Formulae for Arbitrary Positive Measures Fernandes, Andrew D. Atchley, William R. Evol Bioinform Online Original Research 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. Libertas Academica 2007-02-15 /pmc/articles/PMC2674649/ /pubmed/19455218 Text en Copyright © 2006 The authors. http://creativecommons.org/licenses/by/3.0 This article is published under the Creative Commons Attribution By licence. For further information go to: http://creativecommons.org/licenses/by/3.0. (http://creativecommons.org/licenses/by/3.0)
spellingShingle Original Research
Fernandes, Andrew D.
Atchley, William R.
Gaussian Quadrature Formulae for Arbitrary Positive Measures
title Gaussian Quadrature Formulae for Arbitrary Positive Measures
title_full Gaussian Quadrature Formulae for Arbitrary Positive Measures
title_fullStr Gaussian Quadrature Formulae for Arbitrary Positive Measures
title_full_unstemmed Gaussian Quadrature Formulae for Arbitrary Positive Measures
title_short Gaussian Quadrature Formulae for Arbitrary Positive Measures
title_sort gaussian quadrature formulae for arbitrary positive measures
topic Original Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2674649/
https://www.ncbi.nlm.nih.gov/pubmed/19455218
work_keys_str_mv AT fernandesandrewd gaussianquadratureformulaeforarbitrarypositivemeasures
AT atchleywilliamr gaussianquadratureformulaeforarbitrarypositivemeasures

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