| Abel变换数值反演的离散正则化方法 |
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| 引用本文： | 肖庭延,宋金来. Abel变换数值反演的离散正则化方法[J]. 计算物理, 2000, 17(6): 602-610 |
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| 作者姓名： | 肖庭延 宋金来 |
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| 作者单位： | 河北工业大学文理学院, 天津 300130 |
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| 摘 要： | 基于Tikhonov的正则化思想,将Abel变换的理论反演公式与对数值求导的离散正则化处理以及带权的Gauss型积分相结合,给出了Abel变换数值反演的一个新算法,并进行了理论分析与数值实验。结果表明:该算法具有精度高、数值稳定等优点。
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| 关 键 词： | Abel变换 数值反演 离散正则化 带权Gauss积分公式 |
| 收稿时间： | 1999-05-31 |
| 修稿时间： | 2000-01-20 |
A DISCRETE REGULARIZATION METHOD FOR THE NUMERICAL INVERSION OF ABEL TRANSFORM |
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| XIAO TING-yan,SONG Jin-lai. A DISCRETE REGULARIZATION METHOD FOR THE NUMERICAL INVERSION OF ABEL TRANSFORM[J]. Chinese Journal of Computational Physics, 2000, 17(6): 602-610 |
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| Authors: | XIAO TING-yan SONG Jin-lai |
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| Affiliation: | Hebei University of Technology, Tianjin 300130, P R China |
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| Abstract: | Based on Tikhonov's Regularization theory and the theoretical formula of the Abel inversion, a discreted regularization algorithm is proposed for the numerical inversion of Abel transform by integrating the regularized treatment on numerical diffrentiation with the weighted Gauss-type integral. The numerical test and the comparision study are made and show that the algorithm possesses the advantages of high accuracy, good numerical stability and practicability. |
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| Keywords: | Abel transform numerical inversion discrete regularization method weighted Gauss-type integral |
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