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Convergence results on iteration algorithms to linear systems.

Wang Z, Yang C, Yuan Y - ScientificWorldJournal (2014)

Bottom Line: The most important result is that the convergence results have been proved.Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously).Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.

ABSTRACT
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.

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The errors of PSD and Jacobi iteration.
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Related In: Results  -  Collection


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fig2: The errors of PSD and Jacobi iteration.

Mentions: From Figures 2, 3, 4, and 5, the errors of Jacobi iteration are denoted by blue circles and that of MPSD iteration is denoted by red stars. By the figures above, We know that Jacobi iteration is better than backward PSD, JOR, and EMA iteration and is worse than PJ iteration under the values of ω1, ω2, and τ in this example.


Convergence results on iteration algorithms to linear systems.

Wang Z, Yang C, Yuan Y - ScientificWorldJournal (2014)

The errors of PSD and Jacobi iteration.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4061780&req=5

fig2: The errors of PSD and Jacobi iteration.
Mentions: From Figures 2, 3, 4, and 5, the errors of Jacobi iteration are denoted by blue circles and that of MPSD iteration is denoted by red stars. By the figures above, We know that Jacobi iteration is better than backward PSD, JOR, and EMA iteration and is worse than PJ iteration under the values of ω1, ω2, and τ in this example.

Bottom Line: The most important result is that the convergence results have been proved.Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously).Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.

ABSTRACT
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.

Show MeSH