Length Scales in Bayesian Automatic Adaptive Quadrature
Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and min...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2016-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | http://dx.doi.org/10.1051/epjconf/201610802002 |
| _version_ | 1818904677893275648 |
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| author | Adam Gh. Adam S. |
| author_facet | Adam Gh. Adam S. |
| author_sort | Adam Gh. |
| collection | DOAJ |
| description | Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule), mesoscopic (Simpson rule), and macroscopic (quadrature sums of high algebraic degrees of precision). Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived. |
| first_indexed | 2024-12-19T21:11:15Z |
| format | Article |
| id | doaj.art-03ff1bd5dbea48a3bfc20b3f67206bdd |
| institution | Directory Open Access Journal |
| issn | 2100-014X |
| language | English |
| last_indexed | 2024-12-19T21:11:15Z |
| publishDate | 2016-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | EPJ Web of Conferences |
| spelling | doaj.art-03ff1bd5dbea48a3bfc20b3f67206bdd2022-12-21T20:05:29ZengEDP SciencesEPJ Web of Conferences2100-014X2016-01-011080200210.1051/epjconf/201610802002epjconf_mmcp2016_02002Length Scales in Bayesian Automatic Adaptive QuadratureAdam Gh.Adam S.Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule), mesoscopic (Simpson rule), and macroscopic (quadrature sums of high algebraic degrees of precision). Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.http://dx.doi.org/10.1051/epjconf/201610802002 |
| spellingShingle | Adam Gh. Adam S. Length Scales in Bayesian Automatic Adaptive Quadrature EPJ Web of Conferences |
| title | Length Scales in Bayesian Automatic Adaptive Quadrature |
| title_full | Length Scales in Bayesian Automatic Adaptive Quadrature |
| title_fullStr | Length Scales in Bayesian Automatic Adaptive Quadrature |
| title_full_unstemmed | Length Scales in Bayesian Automatic Adaptive Quadrature |
| title_short | Length Scales in Bayesian Automatic Adaptive Quadrature |
| title_sort | length scales in bayesian automatic adaptive quadrature |
| url | http://dx.doi.org/10.1051/epjconf/201610802002 |
| work_keys_str_mv | AT adamgh lengthscalesinbayesianautomaticadaptivequadrature AT adams lengthscalesinbayesianautomaticadaptivequadrature |