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| Titel |
Efficient approximation of the incomplete gamma function for use in cloud model applications |
| VerfasserIn |
U. Blahak |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 3, no. 2 ; Nr. 3, no. 2 (2010-07-23), S.329-336 |
| Datensatznummer |
250000943
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| Publikation (Nr.) |
 copernicus.org/gmd-3-329-2010.pdf |
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| Zusammenfassung |
This paper describes an approximation to the lower incomplete gamma function
γl(a,x) which has been obtained by nonlinear curve fitting. It
comprises a fixed number of terms and yields moderate accuracy (the absolute
approximation error of the corresponding normalized incomplete gamma function
P is smaller than 0.02 in the range 0.9 ≤ a ≤ 45 and x≥0).
Monotonicity and asymptotic behaviour of the original incomplete gamma
function is preserved.
While providing a slight to moderate performance gain on scalar machines
(depending on whether a stays the same for subsequent function evaluations
or not) compared to established and more accurate methods based on series- or
continued fraction expansions with a variable number of terms, a big
advantage over these more accurate methods is the applicability on vector
CPUs. Here the fixed number of terms enables proper and efficient
vectorization. The fixed number of terms might be also beneficial on
massively parallel machines to avoid load imbalances, caused by a possibly
vastly different number of terms in series expansions to reach convergence at
different grid points. For many cloud microphysical applications, the
provided moderate accuracy should be enough. However, on scalar machines and
if a is the same for subsequent function evaluations, the most efficient
method to evaluate incomplete gamma functions is perhaps interpolation of
pre-computed regular lookup tables (most simple example: equidistant tables). |
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