A relaxed projection method using a new linesearch for the split feasibility problem

In this work, we propose a new relaxed projection algorithm for the split feasibility problem with a new linesearch. The proposed method does not require the computation on the matrix inverse and the largest eigenvalue of the matrix. We then prove some weak convergence theorems under suitable conditions in the framework of Hilbert spaces. Finally, we give some numerical examples in signal processing to validate the theoretical analysis results. The obtained results improve the corresponding results in the literature.