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Alternated inertial algorithms for split feasibility problems

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Abstract

We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author.

Notes

  1. Available on the website https://www.tau.ac.il/~becka/home

  2. Download from the website http://www.imageprocessingplace.com/downloads_V3/root_downloads/image_databases/standard_test_images.zip

  3. Access via the website http://www.imm.dtu.dk/~pcha/HNO/HNO.zip

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Acknowledgements

The authors would like to thank the handling editor and the anonymous referee for careful reading and constructive comments, which improved the quality of the manuscript.

Funding

Bing Tan was supported by the China Scholarship Council (CSC No. 202106070094). Xianfu Wang was partially supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. School of Sciences, Southwest Petroleum University, Chengdu, 610500, China

    Bing Tan

  2. Center for Converging Humanities, Kyung Hee University, Seoul, Korea

    Xiaolong Qin

  3. Department of Mathematics, University of British Columbia, Kelowna, B.C., V1V 1V7, Canada

    Bing Tan & Xianfu Wang

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  1. Bing Tan
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  2. Xiaolong Qin
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  3. Xianfu Wang
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Correspondence to Xianfu Wang.

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Tan, B., Qin, X. & Wang, X. Alternated inertial algorithms for split feasibility problems. Numer Algor 95, 773–812 (2024). https://doi.org/10.1007/s11075-023-01589-8

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