摘要
本文研究了Abel变换的数值反演问题.利用Abel变换的理论反演公式与数值求导的积分算子法相结合的方法,对反演公式中奇异积分合理处理,获得Abel变换数值反演的一种算法,并进行了理论分析与数值实验.结果表明该算法具有计算简单、数值稳定等优点.
In this paper, we study the numerical inversion of Abel transform. By uniting the theoretical formula of the Abel inversion and the value derivation＇ s integral operator method, give a reasonable method to deal with singular integral, An algorithm is proposed for the numerical inversion of Abel transform by integral operator method. The numerical test and the comparison study are made, which show that this algorithm possesses calculations simply, good numerical stability and practicability.
出处
《数学杂志》
CSCD
北大核心
2009年第3期383-386,共4页
Journal of Mathematics
基金
中国博士后基金资助项目(No.20080431004)
关键词
Able变换
积分算子
数值反演
奇异积分
Abel transform
integral operator
numerical inversion
singular integral
