Abstract
In this paper, we focus on studying the split feasibility problem (SFP) in Hilbert spaces. Based on the CQ algorithm involving the self-adaptive technique, we introduce a three-step iteration process for approximating the solution of SFP. Then, the convergence results are established under mild conditions. Numerical experiments are provided to show the efficiency in signal processing. Some comparisons to various methods are also provided in this paper.
Highlights
We aim to study the split feasibility problem (SFP), which is to find a point x ∗ ∈ C such that Ax ∗ ∈ Q, (1)
We have introduced new three-step iterative methods involving the self-adaptive technique for the SFP in Hilbert spaces
Weak and strong convergence was discussed under suitable conditions
Summary
We aim to study the split feasibility problem (SFP), which is to find a point x ∗ ∈ C such that Ax ∗ ∈ Q,. In 2002, Byrne [6,7] introduced a new projection algorithm for the SFP It was defined as follows: xn+1 = PC ( xn − τn A∗ ( I − PQ ) Axn ). Mathematics 2019, 7, 712 where PC and PQ are projections onto C and Q, and A∗ denotes the adjoint operator of A This method is often called the CQ algorithm. The relaxed CQ algorithm in a finite-dimentional Hilbert space was introduced by Yang [8] as follows: xn+1 = PCn ( xn − τn ∇ f n ( xn )),. A is a dense matrix and has a large dimension To overcome this difficultly, in 2012, López et al [10] presented a new step-size τn as follows: τn =. Based on the three-step iterative methods, some convergence results, including its efficiency, have been established—see, for example, [18,19,20,21,22,23]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
