Abstract
In this paper, a general splitting method with alternated inertia and its relaxed version are proposed for solving the split equality problem in Hilbert spaces. The proposed methods combine both the relaxation and alternated inertial techniques to speed up the rate of convergence. Furthermore, the methods employ a simple self-adaptive stepsize, which does not require any prior information about the operator norm. Four options of inertial parameters and relaxation parameters are discussed. The weak convergence of the proposed algorithms is analyzed under mild conditions. Finally, two numerical experiments and an application in signal recovery problem are provided to demonstrate the advantages of the proposed algorithms compared to a recent related one.
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The Matlab codes employed to run the numerical experiments are available upon request.
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Communicated by Joerg Fliege.
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Ling, T., Tong, X. & Shi, L. Two general splitting methods with alternated inertia for solving split equality problem in Hilbert spaces. Comp. Appl. Math. 42, 354 (2023). https://doi.org/10.1007/s40314-023-02486-5
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DOI: https://doi.org/10.1007/s40314-023-02486-5