中文摘要：

数学物理反问题是应用数学领域中成长和发展最快的领域之一．反问题大多是不适定的．对于不适定问题的解法已有不少的学者进行探索和研究，Tikhonov正则化方法是一种理论上最完备而在实践上行之有效的方法（参见【5，6，7，8，13】）．Tikhonov正则化方法的核心问题之一是要选取合适的正则化参数（参见【4，13】）．

英文摘要：

In this paper, the multilevel augmentation method, which is a new multiscale method, is applied to solving ill-posed problems. Based on the discrete discrepancy principle, fast algorithms are developed for choosing regularization parameter and solving approximate solutions. Error estimates are given and numerical experiments for solving the first kind integral equations are presented to illustrate the ei~ciency of the algorithm.