Regularized inversion of integral transformations of Mellin convolution type
Regularized inversion of integral transformations of Mellin convolution type
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Mellin 卷积型积分变换的正则逆
DOI：
10.1088/0266-5611/19/5/313
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发表时间：
2003
期刊：
影响因子：
2.1
通讯作者：
V. Kryzhniy
中科院分区：
文献类型：
--
作者：
V. Kryzhniy
本文描述了一种为实值积分变换的反演构建正则化算子的新方法。为以下每个积分变换构建了一组单参数正则化算子：傅里叶正弦和余弦、Hankel、Laplace 和 Meijer。正则化积分变换和精确逆积分变换之间的分析联系对于所有考虑的积分变换都是常见的。它使我们能够进行理论分析，提供有关收敛速度的信息，并反映积分变换数值反演的基本特征。借助傅立叶正弦和拉普拉斯变换的数值示例说明了所提出的实现方法的特征。
The paper describes a new method for building regularizing operators for the inversion of real-valued integral transforms. A one-parametric set of regularizing operators is built for each of the following integral transformations: Fourier sine and cosine, Hankel, Laplace and Meijer. The analytical link between the regularized and exact inverse integral transforms is common for all the integral transformations considered. It allows us to conduct a theoretical analysis that gives information about the rate of convergence, and reflects basic features of the numerical inversion of integral transforms. Features of the proposed method of implementation are illustrated with the help of numerical examples of Fourier sine and Laplace transformations.