scholarly journals A Note on the Inner-Outer Iterative Method for Solving the Linear Equation Ax = b

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Li-Tao Zhang ◽  
Xian-Yu Zuo ◽  
Tong-Xiang Gu ◽  
Yan-Ping Wang ◽  
Yi-Fan Zhang ◽  
...  
Keyword(s):  
Iterative Method ◽  
Linear Equation ◽  
Convergence Property ◽  
Convergence Results ◽  
And Mathematics ◽  
Computers And Mathematics

Recently, Tian et al. [Computers and Mathematics with Applications, 75(2018): 2710-2722] came up with the inner-outer iterative method to solve the linear equation Ax=b and studied the corresponding convergence of the method. In this paper, we improve the main results of the inner-outer method and get weaker convergence results. Moreover, the parameters can be adjusted suitably so that the convergence property of the method can be substantially improved.

scholarly journals The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 607-613 ◽  
Author(s):  
Xiang Wang ◽  
Dan Liao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Convergence Factor ◽  
Gradient Based ◽  
Gradient Type ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Linear Matrix Equations

A hierarchical gradient based iterative algorithm of [L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448] has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

scholarly journals Convergence of Relaxed Matrix Parallel Multisplitting Chaotic Methods forH-Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Li-Tao Zhang ◽  
Jian-Lei Li ◽  
Tong-Xiang Gu ◽  
Xing-Ping Liu
Keyword(s):  
Numerical Experiments ◽  
Convergence Property ◽  
Numerical Examples ◽  
Convergence Results ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant

Based on the methods presented by Song and Yuan (1994), we construct relaxed matrix parallel multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze the convergence of our methods when coefficient matrices areH-matrices or irreducible diagonally dominant matrices. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, we further study some applied convergence results of methods to be convenient for carrying out numerical experiments. Finally, we give some numerical examples, which show that our convergence results are applied and easily carried out.

Making Sense of Groups, Computers, and Mathematics

1995 ◽  
Vol 13 (4) ◽  
pp. 505-523 ◽  
Author(s):  
Lulu Healy ◽  
Stefano Pozzi ◽  
Celia Hoyles
Keyword(s):  
Making Sense ◽  
And Mathematics ◽  
Computers And Mathematics
Sign in / Sign up

Export Citation Format

Share Document