不适定算子方程的预测-校正迭代Tikhonov正则化方法

Iterated Tikhonov regularization is one of the most important regularization methods for solving the ill-posed problems steadily with avoiding the saturation effect of Tikhonov regularization method. But the convergence rate of the Iterated Tikhonov regularization method is relatively slow. According to this, a modified predictor-corrector iterated Tikhonov regularization method is introduced in this paper, with proving the regularity and convergence of the method. While the iterated regularization method can ensure the error estimation always achieve the optimal order. Then we conclude with numerical experiments confirming the modified method can accelerate the convergence rate of the iterative sequences.