We consider Fredholm integral equation of the first kind, present an efficient new iterated Tikhonov method to solve it. The new Tikhonov iteration method has been proved which can achieve the optimal order under a-priori assumption. In numerical experiments, the new iterated Tikhonov regularization method is compared with the classical iterated Tikhonov method, Landweber iteration method to solve the corresponding discrete problem, which indicates the validity and efficiency of the proposed method.

翻译：我们考虑第一类Fredholm积分方程，提出了一种高效的新型迭代Tikhonov方法进行求解。该新型Tikhonov迭代方法已被证明在先验假设下能够达到最优阶。在数值实验中，将新型迭代Tikhonov正则化方法与经典迭代Tikhonov方法、Landweber迭代方法在求解相应离散问题上进行了比较，结果验证了所提方法的有效性和高效性。