The multiple-sets split equality problem is an extended form of the split feasibility problem. It has a wide range of applications in image reconstruction, signal processing, computed tomography, etc. In this paper, we propose a relaxed successive projection algorithm to solve the multiple-sets split equality problem which does not need the prior knowledge of the operator norms, and prove the strong convergence of the algorithm. The numerical examples indicate that the algorithm has good feasibility and effectiveness by comparing with other algorithm.

中文翻译：

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多集分裂等式问题的强收敛松弛连续投影算法

多集分裂相等问题是分裂可行性问题的扩展形式。它在图像重建、信号处理、计算机断层扫描等方面有着广泛的应用。在本文中，我们提出了一种宽松的连续投影算法来解决不需要算子范数的先验知识的多集分裂等式问题。 ，并证明算法的强收敛性。数值算例表明，该算法与其他算法相比具有较好的可行性和有效性。