Analysis of Convergence of Jacobi and Gauss Siedel Method and Error Minimization.

AdikuLydia; Raymond Dominic; OgbajiEkaOche

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Analysis of Convergence of Jacobi and Gauss Siedel Method and Error Minimization.

机译：雅各比和高斯赛德尔方法收敛分析及误差最小化。

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In this research, we will show that neither of the iterative methods always converges. Implying that the Jacobi and Gauss Seidel Methods do not converge often when applied to a system of linear equations yielding a divergent sequence of approximations. In such cases, the method is termed divergent. Therefore for a system of equations to converge, the Diagonal Dominance of the matrix is necessary before applying any iterative method. The error reduction factor will also be discussed in each Iteration in Jacobi and Gauss Seidel method.

机译：在这项研究中，我们将表明既不迭代方法始终会收敛。暗示Jacobi和Gauss Seidel方法不会在应用于线性方程系统时不收敛，产生发散近似序列。在这种情况下，该方法被称为发散。因此，对于汇聚的方程系统，在应用任何迭代方法之前需要矩阵的对角线优势。还将在Jacobi和Gauss Seidel方法中的每次迭代中讨论误差减少因子。

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《International Journal of Engineering Research and Applications》 |2020年第11期|共5页
作者
AdikuLydia; Raymond Dominic; OgbajiEkaOche;
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中图分类工业技术;
关键词
Iterative MethodsConvergenceDivergenceDiagonal DominanceJacobi Method GaussSeidel Method;

机译：迭代方法验验代理人长类代间奥地姆jacobi方法高斯海塞米;

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专利

1. A UNIFIED PROOF FOR THE CONVERGENCE OF JACOBI AND GAUSS-SEIDEL METHODS [J] . Bagnara R. SIAM Review . 1995,第1期

机译：Jacobi方法和高斯-赛德尔方法收敛性的统一证明
2. Shifted Jacobi-Gauss-collocation with convergence analysis for fractional integro-differential equations [J] . Doha E. H., Abdelkawy M. A., Amin A. Z. M., Communications in Nonlinear Science and Numerical Simulation . 2019,第JUNa期

机译：分数阶积分-微分方程的经收敛分析的移位Jacobi-Gauss配置
3. A note on convergence and a posteriori error estimates of the classical Jacobi method [J] . Takuya Tsuchiya, Kensuke Aishima Nonlinear Theory and Its Applications . 2015,第3期

机译：关于经典Jacobi方法的收敛性和后验误差估计的注记
4. Study on the Convergence of Solving Linear Equations by Gauss-Seidel and Jacobi Method [C] . Hongxia Liu, Tianxiang Feng International Conference on Computational Intelligence and Security . 2015

机译：高斯-赛德尔和雅可比法求解线性方程组的收敛性研究
5. ON THE CONVERGENCE OF THE GAUSS-GALERKIN METHOD FOR THE DENSITY OF SOME MARKOV PROCESSES. [D] . HAJ JAFAR, ALI. 1984

机译：关于某些马尔可夫过程的密度的高斯-伽勒金方法的收敛性。
6. An Analysis on Local Convergence of Inexact Newton-Gauss Method for Solving Singular Systems of Equations [O] . Fangqin Zhou -1

机译：求解奇异方程组的不精确牛顿-高斯方法的局部收敛性分析
7. A Unified Proof For The Convergence Of Jacobi And Gauss-Seidel Methods [O] . Roberto Bagnara 1995

机译：Jacobi和Gauss-Seidel方法收敛性的统一证明

Analysis of Convergence of Jacobi and Gauss Siedel Method and Error Minimization.

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