scholarly journals A preconditioned SSOR iteration method for solving complex symmetric system of linear equations

2019 ◽  
Vol 9 (4) ◽  
pp. 483-492
Author(s):  
Tahereh Salimi Siahkolaei ◽  
◽  
Davod Khojasteh Salkuyeh
Keyword(s):  
Iteration Method ◽  
Linear Equations ◽  
Symmetric System ◽  
System Of Linear Equations ◽  
Complex Symmetric

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 Second degree generalized Jacobi iteration method for solving system of linear equations

2016 ◽  
Vol 47 (2) ◽  
pp. 179-192
Author(s):  
Tesfaye Kebede Enyew
Keyword(s):  
Spectral Radius ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Jacobi Iteration ◽  
Optimal Values ◽  
Second Degree

In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1)}=b_{1}[D_{m}^{-1}(L_{m}+U_{m})x^{(n)}+k_{1m}]-a_{1}x^{(n-1)}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ) in comparison with FDJ, FDGJ, SDJ.

Accelerated GPMHSS Method for Solving Complex Systems of Linear Equations

2017 ◽  
Vol 7 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Jing Wang ◽  
Xue-Ping Guo ◽  
Hong-Xiu Zhong
Keyword(s):  
Complex Systems ◽  
Linear Systems ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Splitting Method ◽  
Complex Symmetric Linear Systems ◽  
Systems Of Linear Equations ◽  
Complex Symmetric ◽  
Symmetric Systems

AbstractPreconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

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