中文摘要：

设H1,H2,H3是三个实Hilbert空间,{Ci}mi=1（∈）H1,{Qj}rj=1（∈）H2是非空闭凸集,A：H1 →H3,B：H2→H3是两个有界线性算子.多集分裂等式问题可表述为：找点x∈∩mi=1 Ci,y∈∩rj=1 Qj使得Ax=By.当m=r=1时,多集分裂等式问题简化为分裂等式问题.分裂等式问题及多集分裂等式问题在现实世界中有广泛应用.例如医学图像恢复,计算机断层扫描,放射治疗等等.这篇文章运用一个新的探索方向构造迭代算法来解分裂等式问题及多集分裂等式问题,目的在于提高收敛速度.

英文摘要：

Let H1,H2, Ha be real Hilbert spaces, and let Ci}mi=1（∈）H1,{Qj}rj=1（∈）H2 be nonempty closed convex sets, A：H1 →H3,B：H2→H3 be two bounded and linear operators. The multiple-sets split equality problem is to find x∈∩mi=1 Ci,y∈∩rj=1 Qjsuch that Ax = By. When m = r = 1, the multiple-sets split equality problem reduces to the split equality problem. The applicability of split equality problem and multiple- sets split equality problem covers many situation in real world, for instance medical image reconstruction, computer tomograph and radiation therapy treatment and so on. This paper, by using a new searching direction, presents a variant algorithm to solve the split equality problem and multiple-sets split equality problem aiming at improving convergence.