scholarly journals Mechanical Analogy-based Iterative Method for Solving a System of Linear Equations

2015 ◽  
Vol 15 (08) ◽  
Author(s):  
Yuri Berchun ◽  
Pavel Burkov ◽  
Ayyyna Chirkova ◽  
Sayyyna Prokopieva ◽  
Dmitri Rabkin ◽  
...  
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Mechanical Analogy

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

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.

scholarly journals Second Degree Generalized Successive Over Relaxation Method for Solving System of Linear Equations

2020 ◽  
Vol 12 (1) ◽  
pp. 60-71
Author(s):  
Firew Hailu ◽  
Genanew Gofe Gonfa ◽  
Hailu Muleta Chemeda
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Relaxation Method ◽  
The Other ◽  
System Of Linear Equations ◽  
Convergence Properties ◽  
Numerical Examples ◽  
Successive Over Relaxation ◽  
Number Of Iterations ◽  
Second Degree

In this paper, a second degree generalized successive over relaxation iterative method for solving system of linear equations based on the decomposition  A= Dm+Lm+Um  is presented and the convergence properties of the proposed method are discussed. Two numerical examples are considered to show the efficiency of the proposed method. The results presented in tables show that the Second Degree Generalized Successive Over Relaxation Iterative method is more efficient than the other methods considered based on number of iterations, computational running time and accuracy. Keywords: Second Degree, Generalized Gauss Seidel, Successive over relaxation, Convergence.

The Iterative Method for Solving Parameterized System of Linear Equations with Multiple Right Hand Sides

2018 ◽  
Vol 24 (6) ◽  
pp. 363-370
Author(s):  
M. M. Gourary ◽  
◽  
S. G. Rusakov ◽  
S. L. Ulyanov ◽  
М. М. Zharov ◽  
...  
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Right Hand

scholarly journals Iterative Method for Solving a System of Linear Equations

2017 ◽  
Vol 104 ◽  
pp. 133-137 ◽  
Author(s):  
Mykola Kryshchuk ◽  
Jurijs Lavendels
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
System Of Linear Equations
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