Summation Paths in Clenshaw-Curtis Quadrature

Summation Paths in Clenshaw-Curtis Quadrature

Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion...

Full description

Bibliographic Details
Main Authors: Adam S., Adam Gh.
Format: Article
Language:English
Published: EDP Sciences 2016-01-01
Series:EPJ Web of Conferences
Online Access:http://dx.doi.org/10.1051/epjconf/201610802003
id doaj-7014805b15534690ada0bf446d01cb1e
record_format Article
spelling doaj-7014805b15534690ada0bf446d01cb1e2021-08-02T04:03:14ZengEDP SciencesEPJ Web of Conferences2100-014X2016-01-011080200310.1051/epjconf/201610802003epjconf_mmcp2016_02003Summation Paths in Clenshaw-Curtis QuadratureAdam S.0Adam Gh.1Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH)Laboratory of Information Technologies, Joint Institute for Nuclear ResearchTwo topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.http://dx.doi.org/10.1051/epjconf/201610802003
collection DOAJ
language English
format Article
sources DOAJ
author Adam S.
Adam Gh.
spellingShingle Adam S.
Adam Gh.
Summation Paths in Clenshaw-Curtis Quadrature
EPJ Web of Conferences
author_facet Adam S.
Adam Gh.
author_sort Adam S.
title Summation Paths in Clenshaw-Curtis Quadrature
title_short Summation Paths in Clenshaw-Curtis Quadrature
title_full Summation Paths in Clenshaw-Curtis Quadrature
title_fullStr Summation Paths in Clenshaw-Curtis Quadrature
title_full_unstemmed Summation Paths in Clenshaw-Curtis Quadrature
title_sort summation paths in clenshaw-curtis quadrature
publisher EDP Sciences
series EPJ Web of Conferences
issn 2100-014X
publishDate 2016-01-01
description Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.
url http://dx.doi.org/10.1051/epjconf/201610802003
work_keys_str_mv AT adams summationpathsinclenshawcurtisquadrature
AT adamgh summationpathsinclenshawcurtisquadrature
_version_ 1721242806352084992

Similar Items