The purpose of this article is to propose an algorithm for finding an approximate solution of a split variational inclusion problem for monotone operators. By using inertial method, we get a new and simple algorithm for such a problem. Under standard assumptions, we study the strong convergence theorem of the proposed algorithm. As application, we study the split feasibility problem in real Hilbert spaces. Finally, for supporting the convergence of the proposed algorithm, we also consider several preliminary numerical experiments for solving signal recovery by compressed sensing.

中文翻译：

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解决分裂变分包含问题的新的强收敛

本文的目的是提出一种算法，用于找到单调算子的分裂变分包含问题的近似解。通过使用惯性方法，我们得到了一个新的简单算法来解决这一问题。在标准假设下，我们研究了所提出算法的强收敛定理。作为应用，我们研究了实际希尔伯特空间中的分裂可行性问题。最后，为了支持所提出算法的收敛性，我们还考虑了一些初步的数值实验，用于通过压缩感测解决信号恢复。