The hybird methods of projection-splitting for solving tensor split feasibility problem

Yajun Xie; Changfeng Ma; Yajun Xie; Changfeng Ma

doi:10.3934/math.20231050

AIMS Mathematics

2023, Volume 8, Issue 9: 20597-20611. doi: 10.3934/math.20231050

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Research article

The hybird methods of projection-splitting for solving tensor split feasibility problem

Yajun Xie ¹,
Changfeng Ma ^{2
,
,}

1.
Nanchang Normal College of Applied Technology, Nanchang, 330108, China
2.
Key Laboratory of Digital Technology and Intelligent Computing, Fuzhou University of International Studies and Trade, Fuzhou, 350202, China

Received: 15 April 2023 Revised: 23 May 2023 Accepted: 29 May 2023 Published: 26 June 2023
MSC : 60H35; 65F10

Projection-type methods are studied widely and deeply to solve multiples-sets split feasibility problem. From the perspective of splitting iteration, in this paper, the efficient tensor projection-splitting iteration methods are firstly investigated for solving tensor split feasibility problem, which is properly transformed into a tensor equation by taking advantage of projection operator. Then, accelerated overrelaxation method and symmetric (alternating) accelerated overrelaxation method are further generalized to solve this problem from general system of linear equations to multi-linear systems. Theoretically, the convergence is proven by the analysis of spectral radius of splitting iteration tensor. Numerical experiments demonstrate the efficiency of the presented method.
- tensor split feasibility problem,
- projection-splitting iteration,
- multi-linear systems,
- spectral radius,
- accelerated overrelaxation method
Citation: Yajun Xie, Changfeng Ma. The hybird methods of projection-splitting for solving tensor split feasibility problem[J]. AIMS Mathematics, 2023, 8(9): 20597-20611. doi: 10.3934/math.20231050

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Abstract

Projection-type methods are studied widely and deeply to solve multiples-sets split feasibility problem. From the perspective of splitting iteration, in this paper, the efficient tensor projection-splitting iteration methods are firstly investigated for solving tensor split feasibility problem, which is properly transformed into a tensor equation by taking advantage of projection operator. Then, accelerated overrelaxation method and symmetric (alternating) accelerated overrelaxation method are further generalized to solve this problem from general system of linear equations to multi-linear systems. Theoretically, the convergence is proven by the analysis of spectral radius of splitting iteration tensor. Numerical experiments demonstrate the efficiency of the presented method.

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