求解分裂等式不动点问题的迭代算法

Iterative Algorithm for Solving The Split Equality Fixed Point Problem

近年来,分裂可行性问题已受到人们的广泛关注,并应用于解决许多实际问题,如图像恢复和重构、CT断层扫描和放射疗法计划等。本文针对分裂等式不动点问题的一种迭代算法,改进了步长的选取方式,从而使算法更容易执行。在一定条件下,我们证明了新的迭代算法生成的序列弱收敛于分裂等式不动点问题的解。

In recent years, the split feasibility problem has been widely concerned in many areas and applied to solve many practical problems, such as image restoration and reconstruction,CT scans and radiotherapy plan, etc. In this paper,according to an iterative algorithm for the split equality fixed point problem, we improve the selection method of the step size, which makes the algorithm more easily implemented. Under certain conditions, it is proved that the sequence generated by the new iterative algorithm converges weakly to the solution of the split equality fixed point problem.