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.

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

Research on Iterative Method in Solving Linear Equations on the Hadoop Platform

2013 ◽  
Vol 347-350 ◽  
pp. 2763-2768
Author(s):  
Yi Di Liu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
Engineering Problems ◽  
Jacobi Iteration ◽  
Hadoop Platform ◽  
Iteration Methods ◽  
Division Operation

Solving linear equations is ubiquitous in many engineering problems, and iterative method is an efficient way to solve this question. In this paper, we propose a general iteration method for solving linear equations. Our general iteration method doesnt contain denominators in its iterative formula, and this relaxes the limits that traditional iteration methods require the coefficient aii to be non-zero. Moreover, as there is no division operation, this method is more efficient. We implement this method on the Hadoop platform, and compare it with the Jacobi iteration, the Guass-Seidel iteration and the SOR iteration. Experiments show that our proposed general iteration method is not only more efficient, but also has a good scalability.

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.

Dissertation on “The Rank Technique” and its Application

1965 ◽  
Vol 69 (652) ◽  
pp. 280-283 ◽  
Author(s):  
John Robinson
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Attractive Feature ◽  
System Of Linear Equations ◽  
Initial Development ◽  
The Matrix ◽  
Plane Frames ◽  
General Plane ◽  
Basic Characteristics ◽  
Selection Of

Summary“The Rank Technique” is a method for automatic selection of redundancies in the Matrix Force Method. The method was developed for the complete linear analysis of general plane frames, but is equally applicable to other forms of two- and three-dimensional configurations whose state can be expressed as a system of linear equations. An attractive feature of the method is that the structure is systematically and automatically investigated to determine its basic characteristics. The first point considered is whether the structure is stable or unstable for the prescribed load conditions; if stable, whether determinate or redundant and if redundant, the degree of redundancy. A consistent set of redundants is automatically isolated. For general structures the technique automatically generates the basic and redundant load systems in an indirect manner which can be made readily available, if required. The initial development of “The Rank Technique” was carried out in collaboration with Robert R. Regl and is given in reference 1.

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