关键词: Abel变换, 数值反演, 离散正则化, 带权Gauss积分公式

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.

Key words: Abel transform, numerical inversion, discrete regularization method, weighted Gauss-type integral