Implementation of a superfast algorithm for symmetric positive definite linear equations of displacement rank 2

1994 ◽  
Author(s):  
Thomas K. Huckle
Keyword(s):  
Linear Equations ◽  
Positive Definite ◽  
Symmetric Positive Definite ◽  
Displacement Rank ◽  
Rank 2 ◽  
Superfast Algorithm

scholarly journals A New Version of the Accelerated Overrelaxation Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Shi-Liang Wu ◽  
Yu-Jun Liu
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Positive Definite ◽  
System Of Linear Equations ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Convergence Results ◽  
Aor Method ◽  
Symmetric Positive Definite Matrices ◽  
Overrelaxation Iterative Method

Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant,L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant,H-matrices, symmetric positive definite matrices, andL-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.

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