Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices | Zendy

Gashaye Dessalew | Zendy; Tesfaye Kebede | Zendy; Gurju Awgichew | Zendy; Assaye Walelign | Zendy

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Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices

Author(s) -

Gashaye Dessalew,

Tesfaye Kebede,

Gurju Awgichew,

Assaye Walelign

Publication year - 2021

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2021/8343207

Subject(s) - gauss–seidel method , mathematics , convergence (economics) , rate of convergence , gauss , iterative method , mathematical optimization , computer science , key (lock) , physics , computer security , quantum mechanics , economics , economic growth

This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.

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