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

Author

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  • Gashaye Dessalew
  • Tesfaye Kebede
  • Gurju Awgichew
  • Assaye Walelign

Abstract

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.

Suggested Citation

  • Gashaye Dessalew & Tesfaye Kebede & Gurju Awgichew & Assaye Walelign, 2021. "Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-7, June.
    • Handle: RePEc:hin:jnlaaa:8343207
    DOI: 10.1155/2021/8343207
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