A new preconditioner for Gauss-Seidel method for solving multi-linear systems

被引：4
|
作者：
Xie, Kai [1 ]
Miao, Shu-Xin [1 ]
机构：
[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China
来源：
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2023年 / 40卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Tensor splitting; M-tensor; Multi-linear system; Preconditioned Gauss-Seidel method; M-TENSORS; EIGENVALUE;
D O I：
10.1007/s13160-023-00573-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By combining the preconditioner I + S-a by Li et al. (Appl Numer Math 134:105- 121, 2018) and some elements of the last row of the majorization matrix associated with the coefficient tensor, we propose a new preconditioner and present the corresponding preconditioned Gauss-Seidel method for solving multi-linear systems with M-tensors. Theoretically, we give the convergence and comparison theorems of the proposed preconditioned Gauss-Seidel method. Numerical examples are given to show our theoretical results and the efficiency of the proposed preconditioner.
引用
收藏
页码：1159 / 1173
页数：15
相关论文
共 50 条
  • [21] Backward Gauss-Seidel iteration for preconditioned linear systems
    Wang, Zhuan-De
    Huang, Ting-Zhu
    Yang, Wei
    Advances in Matrix Theory and Applications, 2006, : 426 - 428
  • [22] A new ( I + P) )-like preconditioner for the SOR method for solving multi-linear systems with M-tensors
    Hasanpour, Afsaneh
    Mojarrab, Maryam
    JOURNAL OF MATHEMATICAL MODELING, 2024, 12 (01): : 131 - 144
  • [23] Comparison Of Jacobi Iteration Method And Gauss-Seidel Iteration Method In Solving Fuzzy Linear Equation Systems Using A Computer
    Dihoum, Basma Emhamed
    Abu Flijah, Lutfia Almukhtar
    Al-Qiblawi, Siham Saleh
    Owen, Somaya Ali
    JOURNAL OF ALGEBRAIC STATISTICS, 2022, 13 (02) : 711 - 722
  • [24] A new preconditioned AOR method for solving multi-linear systems
    Chen, Yuhan
    Li, Chenliang
    LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (09): : 1385 - 1402
  • [25] PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS
    Shen, Hailong
    Shao, Xinhui
    Huang, Zhenxing
    Li, Chunji
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2011, 48 (02) : 303 - 314
  • [26] Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations
    Davod Khojasteh Salkuyeh
    NumericalMathematics:AJournalofChineseUniversities(EnglishSeries), 2007, (02) : 164 - 170
  • [27] A doubly stochastic block Gauss-Seidel algorithm for solving linear equations
    Du, Kui
    Sun, Xiao-Hui
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 408 (408)
  • [28] The convergence of the modified Gauss-Seidel methods for consistent linear systems
    Li, W
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 154 (01) : 97 - 105
  • [29] The Gauss-Seidel method with the preconditioner (I plus γG) faster than the generalized SOR method
    Niki, Hiroshi
    Kohno, Toshiyuki
    INFORMATION-AN INTERNATIONAL INTERDISCIPLINARY JOURNAL, 2008, 11 (02): : 151 - 163
  • [30] A New Parallel Gauss-Seidel Method for Poisson Equation
    金元峰
    延边大学学报(自然科学版), 2010, (04) : 301 - 304
12345