Restarted Nonnegativity Preserving Tensor Splitting Methods via Relaxed Anderson Acceleration for Solving Multilinear Systems

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 2061-2079.doi: 10.1007/s42967-024-00439-1

• ORIGINAL PAPERS • Previous Articles

Restarted Nonnegativity Preserving Tensor Splitting Methods via Relaxed Anderson Acceleration for Solving Multilinear Systems

Dongdong Liu¹, Ting Hu¹, Xifu Liu²

1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510520, Guangdong, China;
2. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

Received:2023-11-13 Revised:2024-06-07 Accepted:2024-06-11 Online:2024-10-25 Published:2024-10-25
Contact: Xifu Liu,E-mail:lxf211@cqnu.edu.cn E-mail:lxf211@cqnu.edu.cn
Supported by:
D. Liu was supported in part by the National Natural Science Foundation of China (No. 12101136), the Guangdong Basic and Applied Basic Research Foundations (No. 2023A1515011633), the Project of Science and Technology of Guangzhou (No. 2024A04J2056), the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (No. 2021004), the Open Project of Key Laboratory, School of Mathematical Sciences, Chongqing Normal University (No. CSSXKFKTQ202002). X. Liu was funded by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202100505), the Natural Science Foundation Project of Chongqing of China (Grant No. cstc2021jcyj-msxmX0195), and the Program of Chongqing Innovation Research Group Project in University (Grant No. CXQT19018).

Abstract

Abstract: Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving the multilinear systems. The new method preserves the nonnegativity for every iterative step and improves the existing ones. Furthermore, the convergence analysis of the proposed method is given. The new algorithm performs effectively for numerical experiments.

Key words: Tensor splitting, Multilinear systems, Anderson acceleration, Strong M-tensor

Dongdong Liu, Ting Hu, Xifu Liu. Restarted Nonnegativity Preserving Tensor Splitting Methods via Relaxed Anderson Acceleration for Solving Multilinear Systems[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 2061-2079.

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