A new application methodology of the Fourier transform for rational approximation of the complex error function
A new application methodology of the Fourier transform for rational approximation of the complex error function
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DOI：
10.5539/jmr.v8n1p14
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发表时间：
2015-11
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影响因子：
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通讯作者：
S. Abrarov;B. Quine
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文献类型：
--
作者：
S. Abrarov;B. Quine
本文提出了将傅里叶变换应用于复杂误差函数的一种新方法，得到了有效的有理逼近。具体而言，计算测试表明，仅使用$17$求和项，所获得的复误差函数的有理逼近在最实际重要的域$0 \le x \le 40,000$和${10^{- 4}}y \le{10^2}$上提供了基于hitran的光谱应用所需的平均精度${10^{- 15}}$。由于有理近似不包含依赖于输入参数$x$和$y$的三角函数或指数函数，因此计算速度很快。这样一个例子表明，所考虑的傅里叶变换方法在实际应用中是有利的。
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the obtained rational approximation of the complex error function provides the average accuracy ${10^{ - 15}}$ over the most domain of practical importance $0 \le x \le 40,000$ and ${10^{ - 4}} \le y \le {10^2}$ required for the HITRAN-based spectroscopic applications. Since the rational approximation does not contain trigonometric or exponential functions dependent upon the input parameters $x$ and $y$, it is rapid in computation. Such an example demonstrates that the considered methodology of the Fourier transform may be advantageous in practical applications.