Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (2): 1-6,55.doi: 10.3969/j.issn.1000-5641.2019.02.001

• Mathematics •     Next Articles

Convergence analysis of iterative methods for strictly sub-diagonally dominant linear equations

CAI Jing1,2   

  1. 1. School of Mathematics, Southeast University, Nanjing 211189, China;
    2. College of Science, Huzhou University, Huzhou Zhejiang 313000, China
  • Received:2018-04-02 Online:2019-03-25 Published:2019-03-27

Abstract: The Jacobi iterative method, Guass-Seidel iterative method, and SOR iterative method are commonly used in solving linear equations. When the coefficient matrix of a system of linear equations is strictly sub-diagonally dominant, we demonstrate that the Jacobi, Guass-Seider, and SOR iterative methods are all convergent. By comparing the upper bounds of error for the three iterative methods, we show that the upper bound of error for the Guass-Seidel iterative method is minimal.

Key words: linear equations, iterative method, strictly sub-diagonally dominant, error bounds

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