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