论文标题
菲涅尔积分计算技术
Fresnel Integral Computation Techniques
论文作者
论文摘要
这项工作是Alazah等人先前工作的延伸。 [M。 Alazah，S。N。Chandler-Wilde和S. La Porte，Numerische Mathematik，128（4）：635-661，2014]。我们将菲涅耳积分的计算分为3种情况：截短的泰勒串联，修饰的梯形规则和小型，中和大参数的渐近扩展。这些特殊功能可以准确，有效地计算到任意精度。提供了错误估计值，我们给出了选择各种参数以获得所需精度的系统方法。我们说明了此方法并使用双重精度进行数值验证。
This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor series, modified trapezoid rule and an asymptotic expansion for small, medium and large arguments respectively. These special functions can be computed accurately and efficiently up to an arbitrary precision. Error estimates are provided and we give a systematic method in choosing the various parameters for a desired precision. We illustrate this method and verify numerically using double precision.
