Abstract
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.
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Ling, T., Tong, X. & Shi, L. Modified relaxed CQ methods for the split feasibility problems in Hilbert spaces with applications. J. Appl. Math. Comput. 69, 3067–3094 (2023). https://doi.org/10.1007/s12190-023-01875-7
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DOI: https://doi.org/10.1007/s12190-023-01875-7