Novel accelerated methods of tensor splitting iteration for solving multi-systems

Yajun Xie; Minhua Yin; Changfeng Ma; Yajun Xie; Minhua Yin; Changfeng Ma

doi:10.3934/math.2020180

AIMS Mathematics

2020, Volume 5, Issue 3: 2801-2812. doi: 10.3934/math.2020180

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Research article

Novel accelerated methods of tensor splitting iteration for solving multi-systems

1.
School of Technology, Fuzhou University of International Studies and Trade, Fuzhou 350202, China
2.
College of Business Adminstration, Fujian Jiangxia University, Fuzhou 350108, China
3.
College of Mathematics and Informatics Science & FJKLMAA, Fujian Normal University, Fuzhou 350117, China

Received: 04 November 2019 Accepted: 04 March 2020 Published: 17 March 2020
MSC : 65H10, 65K05, 49M15

Tensor splitting iteration method is a class of popular technique for solving multi-linear systems. In this paper, we present one kind of efficient alternating splitting iteration method, and further generalize accelerated overrelaxation method (AOR) and symmetric accelerated overrelaxation method (SAOR) from linear systems to multi-systems. Then, one type of preconditioned (alternating) tensor splitting method is also applied for solving multi-systems. Numerical experiments illustrate the efficiency of the provided methods.
- multi-systems,
- tensor alternating splitting iteration,
- accelerated overrelaxation method,
- symmetric accelerated overrelaxation,
- preconditioned technique
Citation: Yajun Xie, Minhua Yin, Changfeng Ma. Novel accelerated methods of tensor splitting iteration for solving multi-systems[J]. AIMS Mathematics, 2020, 5(3): 2801-2812. doi: 10.3934/math.2020180

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Abstract

Tensor splitting iteration method is a class of popular technique for solving multi-linear systems. In this paper, we present one kind of efficient alternating splitting iteration method, and further generalize accelerated overrelaxation method (AOR) and symmetric accelerated overrelaxation method (SAOR) from linear systems to multi-systems. Then, one type of preconditioned (alternating) tensor splitting method is also applied for solving multi-systems. Numerical experiments illustrate the efficiency of the provided methods.

References

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