ScholarLens Back to search
2020•Journal of the Nigerian Mathematical SocietyOpen access

SECOND REFINEMENT OF GENERALIZED JACOBI ITERATIVE METHOD FOR SOLVING LINEAR SYSTEM OF EQUATIONS

Tesfaye Kebede Enyew, Gurju Awgichew, H. Haile, Gashaye Dessalew Abie

Open full text 2 citations

Abstract

The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. In this paper, we present the new method which is called secondrefinement of generalized Jacobi (SRGJ) method for solving linear system of equations. This new method is the fastest method to converge to the exact solution as compared with Jacobi (J), refinement of Jacobi (RJ), generalized of Jacobi and refinement of generalized Jacobi (RGJ) method by considering strictly diagonally dominant (SDD), symmetric positive definite (SPD) and M-matrices. It is verified by checking the number of iterations and rate of convergence. The SRGJ method can be applied to solve ODE and PDE problems when finite difference method results system of linear equations with its coefficient matrices are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices.

About this research paper

What this paper is about

The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. In this paper, we present the new method which is called secondrefinement of generalized Jacobi (SRGJ) method for solving linear system of equations. This new method is the fastest method to converge to the exact solution as compared with Jacobi (J), refinement of Jacobi (RJ), generalized of Jacobi and refinement of generalized Jacobi (RGJ) method by considering strictly diagonally dominant (SDD), symmetric positive definite (SPD) and M-matrices. It is verified by checking the number of iterations and rate of convergence. The SRGJ method can be applied to solve ODE and PDE problems when finite difference method results system of linear equations with its coefficient matrices are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. In this paper, we present the new method which is called secondrefinement of generalized Jacobi (SRGJ) method for solving linear system of equations. This new method is the fastest method to converge to the exact solution as compared with Jacobi (J), refinement of Jacobi (RJ), generalized of Jacobi and refinement of generalized Jacobi (RGJ) method by considering strictly diagonally dominant (SDD), symmetric positive definite (SPD) and M-matrices. It is verified by checking the number of iterations and rate of convergence. The SRGJ method can be applied to solve ODE and PDE problems when finite difference method results system of linear equations with its coefficient matrices are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices.

Key concepts: Jacobi method, Jacobi eigenvalue algorithm, Mathematics, Gauss–Seidel method, Diagonally dominant matrix, Applied mathematics, Iterative method, Ode

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
SECOND REFINEMENT OF GENERALIZED JACOBI ITERATIVE METHOD FOR SOLVING LINEAR SYSTEM OF EQUATIONS — Research Paper | ScholarLens