Randomized Average Kaczmarz Algorithm for Tensor Linear Systems

Wendi Bao (), Feiyu Zhang, Weiguo Li, Qin Wang and Ying Gao
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Wendi Bao: College of Science, China University of Petroleum, Qingdao 266580, China
Feiyu Zhang: College of Science, China University of Petroleum, Qingdao 266580, China
Weiguo Li: College of Science, China University of Petroleum, Qingdao 266580, China
Qin Wang: College of Science, China University of Petroleum, Qingdao 266580, China
Ying Gao: College of Science, China University of Petroleum, Qingdao 266580, China

Mathematics, 2022, vol. 10, issue 23, 1-24

Abstract: For solving tensor linear systems under the tensor–tensor t-product, we propose the randomized average Kaczmarz (TRAK) algorithm, the randomized average Kaczmarz algorithm with random sampling (TRAKS), and their Fourier version, which can be effectively implemented in a distributed environment. We analyzed the relationships (of the updated formulas) between the original algorithms and their Fourier versions in detail and prove that these new algorithms can converge to the unique least F-norm solution of the consistent tensor linear systems. Extensive numerical experiments show that they significantly outperform the tensor-randomized Kaczmarz (TRK) algorithm in terms of both iteration counts and computing times and have potential in real-world data, such as video data, CT data, etc.

Keywords: tensor linear system; randomized average Kaczmarz method; T-product; least-norm problem; Fourier domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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