The search for alternative algorithms of the iteration method on a system of linear equation

Authors

  • Aam Jon Mintase Tarigan Universitas Sumatera Utara, Medan, Indonesia
  • Mardiningsih Universitas Sumatera Utara, Medan, Indonesia
  • Saib Suwilo Universitas Sumatera Utara, Medan, Indonesia

DOI:

10.33395/sinkron.v7i4.11817

Keywords:

Alternative Iteration , Algorithm , Matrix

Abstract

The system of linear equations is a set of linear equations consisting of coefficients and variables. The coefficients in the system of linear equations exist in the form of real numbers and some are complex numbers. The system of linear equations has some form of solving or solution, ie a single solution, many solutions and no solutions. One of the most common problems encountered in systems of linear equations. Using modern mathematical methods, often a complex problem can be reduced to a system of linear equations.There are basically two groups of methods that can be used to solve a linear equation. The first method is known as the direct method, ie the method that searches for the completion of a linear equation in finite step. These are guaranteed to work and are recommended for general use. The second group is known as the indirect method or the method of iteration, which starts from an early settlement. Then try to fix almost in infinity, but convergent steps. The iterative methods are used to solve large Linear Equations Systems. And the proportion of zero is large, as are many systems encountered in the Linear Equation System. Therefore it takes an Alternative Algorithm in Iteration Method

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References

Bagnara, R.A. Unified Proof For the Convergence of Jacobi and Gauss- Seidel Methods. Society for Industrial and Applied Mathematica. Vol. 37,

Daftardar,G. and Javari,H.(2005). Adomian decomposition: a tool for solving a system of fractional differentialequations, J. Math. Anal. Appl. 301 508–518.

Evans, D. J., Martins, M. M. dan Trigo, M. E. (2001). The AOR IterativeMethod for New Preconditioned Linear System. Journal of Computational Applied Math. 132, 461-466.

Jayachamarajandra,S.(2011). Eigenvalues of tridiagonal matrix using StrumSeguence and Gerschgorin theorem,Internasional Journal

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How to Cite

Tarigan, A. J. M., Mardiningsih , M. ., & Suwilo, S. . (2022). The search for alternative algorithms of the iteration method on a system of linear equation. Sinkron : Jurnal Dan Penelitian Teknik Informatika, 7(4), 2124-2424. https://doi.org/10.33395/sinkron.v7i4.11817