Modified relaxed CQ methods for the split feasibility problems in Hilbert spaces with applications.

In this paper, four modified versions of relaxed CQ algorithms are proposed for solving the split feasibility problems (SFP) in infinite-dimensional real Hilbert spaces. The methods are based on replacing the projection to the half-space with that to the intersection of two half-spaces. The convergence speed is accelerated as the algorithms make use of the previous half-spaces. The stepsize is determined dynamically without requiring any prior information about the operator norm. Furthermore, the proposed algorithms are proven to converge strongly to the minimum-norm solution of the SFP. As an application, we apply our results to signal recovery problems. [ABSTRACT FROM AUTHOR]