中文摘要：

H_1,H_2,H_3是实希尔伯特空间,CH_1,QH_2是两个非空闭凸子集,A H_1→H_3,B：H_2→H_3是两个有界线性算子.我们的兴趣是解决下面的问题：找x∈C,y∈Q使得Ax=By.Moudafi提出了同步迭代算法（SIM）来解决分裂等式问题.为了利用同步迭代算法（SIM）,在计算步长时需要知道有界线性算子的范数,这个范数的数值计算中难以实现.本文的主要目的是介绍一种选择步长的方式使得同步迭代算法的完成不需要任何算子的范数.同时,松弛的同步迭代算法也被提出.最后,论文通过数值试验得出这种步长的选择方法使得并行迭代算法收敛更快.

英文摘要：

Let H1, H2, H3 be real Hilbert spaces, C C H1, Q c H2 be two nonempty close convex sets, A ：/-/1 → H3, B ： H2 →H3 be two bounded linear operators. Our interest is solving the following problem：find x ∈ C, y ∈ Q such that Ax = By.Moudafi introduced a simultaneous iterative method（SIM） for this split equality prob- lem. However, to employ SIM, one needs to know a prior the norm of bounded linear operator. The purpose of this paper is to introduce a way of selecting the stepsizes such that the implementation of SIM does not need any prior information about the operator norm. At the same time, a relaxed SIM algorithm was proposed. Finally, This paper concluded that new stepsizes made the simultaneous iterative method converge faster through the numerical experiment.