In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a 2D Inverse Potential Problem, ii) an Image Deblurring Problem; the computational efficiency of the method is compared with standard implementations of the iT method.

翻译：本文提出并分析了一种隐式两点型方法（或称惯性方法），用于获取线性病态算子方程的稳定近似解。该方法基于迭代Tikhonov（iT）方案。我们建立了精确数据情形下的收敛性，以及含噪数据情形下的稳定性和半收敛性。数值实验方面考虑了：i）二维逆势问题，ii）图像去模糊问题；并将该方法的计算效率与iT方法的标准实现进行了比较。