ABSTRACT

In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method.

中文翻译：

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新惯性法求解共零点问题的收敛性分析

摘要

在本文中，我们提出了一种新的具有交替惯性步长的迭代方法来解决真实希尔伯特空间中的分裂公共零点问题。我们获得了所提出的迭代算法的弱收敛性。此外，我们为分裂公共零点问题引入了有界线性正则性的概念，并在一些温和的假设下获得了新算法的线性收敛性。最后，我们提供了一些数值示例来证明所提出方法的性能和效率。