In this paper, we introduce two inertial accelerated algorithms for solving the split common fixed-point problem of directed operators in real Hilbert space. The proposed iterative algorithms combine the primal-dual method and the inertial method with the self-adaptive stepsizes such that the implementation of our algorithms does not need any prior information about bounded linear operator norms. Under suitable conditions, the weak and strong convergence results of the algorithms are obtained. Numerical results which involve image restoration problems are reported to show the effectiveness of the proposed algorithms.

中文翻译：

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定向算子的分解公共不动点问题的惯性加速算法。

在本文中，我们介绍了两种惯性加速算法，用于解决实际希尔伯特空间中有向算子的分裂公共不动点问题。所提出的迭代算法将原始对偶方法和惯性方法与自适应步长相结合，从而使我们算法的实现不需要关于有界线性算子范数的任何先验信息。在合适的条件下，获得了算法的弱收敛性和强收敛性。据报道涉及图像恢复问题的数值结果表明了所提出算法的有效性。