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Strong convergence of alternated inertial CQ relaxed method with application in signal recovery

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Abstract

This article proposes a strong convergence CQ relaxed iterative method with alternated inertial extrapolation step in a real Hilbert space. The propose method converges strongly under some suitable and easy to verify assumptions. Moreover, the proposed method does not require the prior knowledge of the operator norm or estimate of the matrix norm. Instead, the stepsize is self-adaptive with a simple selection procedure that does not involve any linesearch procedure. Numerical experiments to illustrate the computational performance together with implementation of the proposed method in signal recovery application is presented. Additionally, comparison of the method with some existing iterative methods in the literature is performed.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. The first, third and fourth authors were supported by Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi, Thailand (Grant nos. 38/2018, 37/2018 and 16/2018, respectively). Moreover, this research was funded by King Mongkut’s University of Technology North Bangkok, Contract no. KMUTNB-65-KNOW-28.

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Authors and Affiliations

  1. KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory Science Laboratory Building Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Jamilu Abubakar, Poom Kumam, Guash Haile Taddele & Abdulkarim Hassan Ibrahim

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  3. KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  4. Department of Mathematics, Faculty of Sciences, Usmanu Danfodiyo University, Sokoto, Sokoto, Nigeria

    Jamilu Abubakar

  5. Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok, Thailand

    Kanokwan Sitthithakerngkiet

Authors
  1. Jamilu Abubakar
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  2. Poom Kumam
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  3. Guash Haile Taddele
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  4. Abdulkarim Hassan Ibrahim
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  5. Kanokwan Sitthithakerngkiet
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Correspondence to Poom Kumam.

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Communicated by Antonio José Silva Neto.

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This project was supported by Petchra Pra Jom Klao Doctoral Academic Scholarship for Ph.D. Program at KMUTT. Moreover, this research was funded by Thailand Science Research and Innovation Fund, and King Mongkut’s University of Technology North Bangkok with Contract no. KMUTNB-BasicR-64-22.

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Abubakar, J., Kumam, P., Taddele, G.H. et al. Strong convergence of alternated inertial CQ relaxed method with application in signal recovery. Comp. Appl. Math. 40, 310 (2021). https://doi.org/10.1007/s40314-021-01567-7

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  • DOI: https://doi.org/10.1007/s40314-021-01567-7

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