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Optimized implementations of rational approximations—a case study on the Voigt and complex error function
Schreier, Franz and Kohlert, Dieter (2008) Optimized implementations of rational approximations—a case study on the Voigt and complex error function. Computer Physics Communications, 179 (7), pp. 457-465. Elsevier. DOI: 10.1016/j.cpc.2008.04.012.
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Official URL: http://www.sciencedirect.com/science/journal/00104655
Abstract
Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued special functions. For the complex error function w (x + i y ), whose real part is the Voigt function K (x, y ), the rational approximation developed by Hui, Armstrong, and Wray [Rapid computation of the Voigt and complex error functions, J. Quant. Spectrosc. Radiat. Transfer 19 (1978) 509–516] is investigated. Various optimizations for the algorithm are discussed. In many applications, where these functions have to be calculated for a large x grid with constant y, an implementation using real arithmetic and factorization of invariant terms is especially efficient.
| Document Type: | Article | ||||||
|---|---|---|---|---|---|---|---|
| Title: | Optimized implementations of rational approximations—a case study on the Voigt and complex error function | ||||||
| Authors: |
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| Date: | September 2008 | ||||||
| Journal or Publication Title: | Computer Physics Communications | ||||||
| Refereed publication: | Yes | ||||||
| In ISI Web of Science: | Yes | ||||||
| Volume: | 179 | ||||||
| DOI: | 10.1016/j.cpc.2008.04.012 | ||||||
| Page Range: | pp. 457-465 | ||||||
| Publisher: | Elsevier | ||||||
| Status: | Published | ||||||
| Keywords: | Plasma dispersion function, Hjerting function, Rational approximation, Continued fractions, Polynomial evaluation | ||||||
| HGF - Research field: | Aeronautics, Space and Transport | ||||||
| HGF - Program: | Space | ||||||
| HGF - Program Themes: | V - no assignement | ||||||
| DLR - Research area: | Space | ||||||
| DLR - Program: | W EO - Erdbeobachtung | ||||||
| DLR - Research theme (Project): | W - Vorhaben Entwicklung von Atmosphärenprozessoren (old) | ||||||
| Location: | Oberpfaffenhofen | ||||||
| Institutes and Institutions: | Remote Sensing Technology Institute > Atmospheric Processors | ||||||
| Deposited By: | Dr.rer.nat. Franz Schreier | ||||||
| Deposited On: | 14 Oct 2008 | ||||||
| Last Modified: | 27 Apr 2009 15:14 |
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