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Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery

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  • Cholamjiak, Watcharaporn
  • Dutta, Hemen

Abstract

In this paper, we introduce a new parallel algorithm by combining viscosity modification with parallel inertial two steps forward-backward splitting methods for approximating a solution of common inclusion problems. The strongly convergent theorems are established under some suitable conditions in Hilbert spaces. The applicability and advantages of the new parallel algorithm are presented by using to solve signal recovering problem in compressed sensing. The efficiency of the algorithm is shown by comparing it with some previous parallel algorithms.

Suggested Citation

  • Cholamjiak, Watcharaporn & Dutta, Hemen, 2022. "Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000698
    DOI: 10.1016/j.chaos.2022.111858
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    References listed on IDEAS

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    1. Heinz H. Bauschke & Patrick L. Combettes, 2001. "A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 248-264, May.
    2. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    3. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
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    Cited by:

    1. Suthep Suantai & Kunrada Kankam & Damrongsak Yambangwai & Watcharaporn Cholamjiak, 2022. "A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    2. Watchareepan Atiponrat & Pariwate Varnakovida & Pharunyou Chanthorn & Teeranush Suebcharoen & Phakdi Charoensawan, 2023. "Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations," Mathematics, MDPI, vol. 11(15), pages 1-20, August.

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