We study the forward-backward-forward splitting method with alternated inertial step in this paper. We consider under-relaxation and over-relaxation approaches to the proposed method and obtain weak convergence results in both cases in real Hilbert spaces. Linear convergence alongside priori and apriori error estimates are obtained under some standard assumptions. Finally, we give some numerical implementations and comparisons to support the theoretical analysis.

中文翻译：

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具有交替惯性步长的宽松前-后-前算法：弱收敛和线性收敛

本文研究了具有交替惯性步长的前-后-前分裂方法。我们考虑了所提出方法的欠松弛和过松弛方法，并且在真实希尔伯特空间中的两种情况下都获得了弱收敛结果。在一些标准假设下获得与先验和先验误差估计一起的线性收敛。最后，我们给出了一些数值实现和比较来支持理论分析。