Optimized implementations of rational approximations—a case study on the Voigt and complex error function |
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Authors: | Franz Schreier Dieter Kohlert |
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Affiliation: | a DLR—German Aerospace Center, Remote Sensing Technology Institute, Oberpfaffenhofen, 82234 Weßling, Germany b Regensburg University of Applied Sciences, Department of Electrical Engineering, Seybothstr. 2, 93053 Regensburg, Germany |
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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+iy), 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. |
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Keywords: | 02 30 Mv 02 60 -x 02 70 -c 31 15 -p |
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