scholarly journals Improving Results on Convergence of AOR Method

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Guangbin Wang ◽  
Ting Wang ◽  
Yanli Du

We present some sufficient conditions on convergence of AOR method for solvingAx=bwithAbeing a strictly doublyαdiagonally dominant matrix. Moreover, we give two numerical examples to show the advantage of the new results.

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guangbin Wang ◽  
Ting Wang

We discuss the convergence of the GAOR method to solve linear system which occurred in solving the weighted linear least squares problem. Moreover, we present one convergence theorem of the GAOR method when the coefficient matrix is a strictly doublyαdiagonally dominant matrix which is a nonsingularH-matrix. Finally, we show that our results are better than previous ones by using four numerical examples.


2019 ◽  
Vol 11 (6) ◽  
pp. 1
Author(s):  
Xin Li ◽  
Mei Qin

In this paper, we present a new practical criteria for H-matrix based on γ-diagonally dominant matrix. In order to make the judgment conditions convenient and effective, we give two new definitions, one is called strong and weak diagonally dominant degree, the other is called the sum of non-principal diagonal element for the matrix. Further, we obtain a new practical method for the determination of the H-matrix by combining the properties of γ-diagonally dominant matrix, constructing positive diagonal matrix, and adding the appropriate parameters. Finally, we offer numerical examples to verify the validity of the judgment conditions, corresponding numerical examples compared the new criteria and the existing results are presented to verify the advantages of the new determination method.


2014 ◽  
Vol 1049-1050 ◽  
pp. 1316-1319
Author(s):  
Ming Da Zhang

Generalized strictly diagonally dominant matrix is very important in computing mathematics and matrix theory, many articles are searching simple and practical identification of generalized strictly diagonally dominant matrix. In this paper, using the concept of diagonal dominance, some sufficient conditions for generalized strictly diagonally dominant matrices are given.


2014 ◽  
Vol 651-653 ◽  
pp. 2207-2210
Author(s):  
Ming Da Zhang

Generalized strictly diagonally dominant matrix is very important in computing mathematics and matrix theory, many articles are searching simple and practical identification of generalized strictly diagonally dominant matrix. In this paper, using the concept of diagonal dominance, some sufficient conditions for generalized strictly diagonally dominant matrices are given.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Gashaye Dessalew ◽  
Tesfaye Kebede ◽  
Gurju Awgichew ◽  
Assaye Walelign

In this paper, we present refinement of multiparameters overrelaxation (RMPOR) method which is used to solve the linear system of equations. We investigate its convergence properties for different matrices such as strictly diagonally dominant matrix, symmetric positive definite matrix, and M-matrix. The proposed method minimizes the number of iterations as compared with the multiparameter overrelaxation method. Its spectral radius is also minimum. To show the efficiency of the proposed method, we prove some theorems and take some numerical examples.


2002 ◽  
Vol 79 (7) ◽  
pp. 841-848 ◽  
Author(s):  
Xijuan Guo ◽  
Zhihua Liu Chao Jia ◽  
Chao Jia

2016 ◽  
Vol 14 (1) ◽  
pp. 747-760
Author(s):  
Cheng-yi Zhang ◽  
Zichen Xue ◽  
Shuanghua Luo

AbstractIt is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.


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