| In 1994,Censor and Elfving[1]proposed the split feasibility problem in the problems of the phase recovery and medical image reconstruction.Some achievements have been made about this problem.In 2013,Moudafi[13]generalized the split feasibility problem and proposed the split equality problem for the first time.In order to solve the problem,many authors who had proposed all kinds of algorithms to solve it,and proved the strong convergence or weak convergence of the algorithms,but few authors consider the convergence rate of algorithms.Convergence rate means how fast the sequences generated by the algorithm converge to their limit points.Consequently,it is worth further research.This paper mainly studies the following content.1.The multiple-sets split feasibility problem(which is the special case of Multiple-sets split equality problem):In this paper,we proposed a new three-step iterative algorithm and proved its strongly convergence.The algorithm is better than the previous algorithm,and numerical results are provided to prove the effectiveness of the algorithm.2.The multiple-sets split equality problem:In this paper,we involved the concept of bounded linear regularity and bounded Holder regularity about the multiple-sets split equality problem in chapters 3 and 4,respectively,and we construct some mild conditions to ensure the linear convergence or sublinear convergence of our proposed algorithm.Finally,we provide the numerical results to show the effectiveness of the algorithm. |
