修改的CQ算法强收敛定理在分裂可行问题中的应用

Convergence of the modified CQ algorithm and its application in split feasibility problem

2001年,C.Byrne提出了CQ算法来解决分裂可行问题,但是只能得到弱收敛.本文的目的是改进他的算法,使得迭代序列能够强收敛.不同于以前的论文,我们在迭代序列里取定了一个定点,每次迭代里都与该向量做和,这样的做法使得迭代序列更容易收敛.类似的做法在Xu HK的文章里出现过,但是本文的迭代算法是第一次提出.

In the year 2001,CQ Algorithm was proposed by C Byrne,but only weak convergence was obtained.The purpose of the paper is to modify his algorithm,so that strong convergence is obtained.The distinction of the paper is that we set a fixed point,add it to the iterative sequence each time.Convergence of the algorithm is thus facilitated.This method has been used in Xu′s paper,but the algorithm is originally made and first proposed.