Geodesic
Alternated inertial fixed point algorithms
Minimax theory and its applications, Tome 9 (2024) no. 2
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We study a weakly convergent fixed point algorithm with alternated inertial step to approximate a common fixed point of a sequence of mappings of nonexpansive type in a real Hilbert space. We present convergence analysis for the proposed algorithm under mild assumptions. Then, we apply the results to iterative algorithms of type alternating projection, forward-backward and primal-dual splitting and derive some convergence results. To demonstrate the effectiveness of our proposed algorithm, we present numerical comparisons of the algorithm with the existing ones.
Mots-clés : Nonexpansive mapping, fixed point, alternated inertial term, weak convergence, primal dual splitting algorithm, Hilbert space 
@article{MTA_2024_9_2_a11,
     author = {Shin-ya Matsushita},
     title = {Alternated inertial fixed point algorithms},
     journal = {Minimax theory and its applications},
     year = {2024},
     volume = {9},
     number = {2},
     zbl = {07929252},
     url = {http://geodesic.mathdoc.fr/item/MTA_2024_9_2_a11/}
}
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Shin-ya Matsushita. Alternated inertial fixed point algorithms. Minimax theory and its applications, Tome 9 (2024) no. 2. http://geodesic.mathdoc.fr/item/MTA_2024_9_2_a11/