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

• ORIGINAL PAPERS • 上一篇    

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

Dongdong Liu1, Ting Hu1, Xifu Liu2   

  1. 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
  • 收稿日期:2023-11-13 修回日期:2024-06-07 接受日期:2024-06-11 出版日期:2024-10-25 发布日期:2024-10-25
  • 通讯作者: Xifu Liu,E-mail:lxf211@cqnu.edu.cn E-mail:lxf211@cqnu.edu.cn
  • 基金资助:
    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).

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

Dongdong Liu1, Ting Hu1, Xifu Liu2   

  1. 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).

摘要: 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.

关键词: Tensor splitting, Multilinear systems, Anderson acceleration, Strong M-tensor

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