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

2013 ◽  
Author(s):  
Yi-di Liu
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Hadoop Platform

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.

An iterative method for solving partitioned linear equations

Computing ◽  
1975 ◽  
Vol 15 (4) ◽  
pp. 357-363 ◽  
Author(s):  
A. S. Kydes ◽  
R. P. Tewarson
Keyword(s):  
Iterative Method ◽  
Linear Equations

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 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
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