The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results.

中文翻译：

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等分公共零点问题的线性收敛性及其在优化问题中的应用

本文的目的是提出一种求解分裂等式公共零点问题（SECNP）的迭代算法，该算法将为希尔伯特空间中一类最大单调算子的有限族找到公共零点集的元素。我们介绍了SECNP的有界线性规则性的概念，并构造了几个充分的条件以确保算法的线性收敛。此外，给出了一些数值实验来检验我们的结果的有效性。