An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery

This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some num...

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Published inAIMS mathematics Vol. 7; no. 2; pp. 1775 - 1790
Main Authors Jun-on, Nipa, Suparatulatorn, Raweerote, Gamal, Mohamed, Cholamjiak, Watcharaporn
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
g-nonexpansive
inertial extrapolation
numerical discussion
parallel algorithm
weak convergence
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022102

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Abstract This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.
AbstractList This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.
Author Cholamjiak, Watcharaporn
Jun-on, Nipa
Suparatulatorn, Raweerote
Gamal, Mohamed
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CorporateAuthor School of Science, University of Phayao, Phayao 56000, Thailand
Faculty of Sciences, Lampang Rajabhat University, Lampang 52100, Thailand
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
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StartPage 1775
SubjectTerms g-nonexpansive
inertial extrapolation
numerical discussion
parallel algorithm
weak convergence
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Title An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery
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