Fast Computation of Singular Oscillatory Fourier Transforms
Fast Computation of Singular Oscillatory Fourier Transforms
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DOI：
10.1155/2014/984834
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发表时间：
2014-07
影响因子：
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通讯作者：
Hongchao Kang;Xinping Shao
中科院分区：
文献类型：
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作者：
Hongchao Kang;Xinping Shao
我们考虑奇异振荡傅里叶变换的数值计算问题，其中.在用最陡下降路径代替原积分区间的基础上，如果在包含[，]的复数区域内是解析的，则积分的计算可以转化为对被积函数在[0，∞)上的两个积分进行积分的问题，被积函数不振荡且指数衰减快，利用广义高斯拉盖尔求积规则可以有效地计算该问题。数值实验和理论结果都证明了该方法的有效性和有效性。更重要的是，本文提出的方法也是对Kang和Xong(2011)提出的Filon型方法和Clenshaw-Curtis-Filon型方法以及Kang等人提出的Chebyshev展开方法的极大改进。(2013)，用于计算上述积分。
We consider the problem of the numerical evaluation of singular oscillatory Fourier transforms , where . Based on substituting the original interval of integration by the paths of steepest descent, if is analytic in the complex region containing [, ], the computation of integrals can be transformed into the problems of integrating two integrals on [0, ∞) with the integrand that does not oscillate and decays exponentially fast, which can be efficiently computed by using the generalized Gauss Laguerre quadrature rule. The efficiency and the validity of the method are demonstrated by both numerical experiments and theoretical results. More importantly, the presented method in this paper is also a great improvement of a Filon-type method and a Clenshaw-Curtis-Filon-type method shown in Kang and Xiang (2011) and the Chebyshev expansions method proposed in Kang et al. (2013), for computing the above integrals.