Second Refinement of Jacobi Iterative Method for Solving Linear System of Equations

Tesfaye Kebede Eneyew, Gurju Awgichew, Eshetu Haile, Gashaye Dessalew Abie

Abstract


In this paper, the new method called second refinement of Jacobi (SRJ) method for solving linear system of equations is proposed. The method can be used to solve ODE and PDE problems where the problems are reduced to linear system of equations with coefficient matrices which are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices. In this case, our new method minimizes the number of iterations as well as spectral radius and increases rate of convergence. Few numerical examples are considered to show the efficiency of SRJ over Jacobi (J) and refinement of Jacobi (RJ) methods.

Keywords


Jacobi Iterative method; Refinement of Jacobi method; GJ; RGJ; Symmetric

Full Text:

PDF

References


A. Laskar and S. Behera, “Refinement of iterative methods for the solution of system of linear equations ax=b,” IOSR Journal of Mathematics (IOSRJM), vol. 10, no. 3, pp. 70–73, 2014.

R. Varga, Matrix iterative analysis. Springer Science & Business Media, 2009, vol. 27.

B. Datta, Numerical linear algebra and applications. Siam, 2010, vol. 116.

W. Hackbusch, Iterative solution of large sparse systems of equations. Springer, 1994, vol. 95.

Y. Saad, Iterative methods for sparse linear systems. siam, 2003, vol. 82.

D. Young, Iterative solution of large linear systems. Elsevier, 2014.




DOI: http://dx.doi.org/10.12962/j24775401.v5i2.4311

Refbacks

  • There are currently no refbacks.



View My Stats


Creative Commons License
International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/ijcsam.