Refinements of Generalized Jacobi Method: A Higher-Order Approach

Authors

  • Urboshi Hazarika Assam University, India
  • Samira Behera Assam University, India

DOI:

https://doi.org/10.22232/stj.2024.12.02.18

Keywords:

System of Linear Equations, Iterative methods, Jacobi; Generalized Jacobi, SDD matrix, M-matrix, Banded matrix

Abstract

This study presents a comparative analysis of the pth Refinement of Generalized Jacobi method, focusing on its derivation, convergence properties, and numerical performance. We first derive the Third Refinement of Generalized Jacobi method and establish a general formula applicable to any pth Refinement. The analysis rigorously proves convergence for various types of matrices, including Strictly Diagonally Dominant (SDD) and M-matrices. Additionally, we demonstrate that the convergence rate of the (p + 1)th Refinement surpasses that of the pth Refinement, assuming the Generalized Jacobi method converges. Numerical examples are provided to support our theoretical findings, showcasing the improved convergence rates of the (p + 1)th Refinement compared to the pth Refinement. These results underline the advantages of higher-order refinements in the Generalized Jacobi method.

Author Biographies

Urboshi Hazarika, Assam University, India

Department of Mathematics

Samira Behera, Assam University, India

Department of Mathematics

References

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Cover page of Science & Technology Journal (STJ), Volume 12, Number 2, June 2024, published by Mizoram University

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Published

2025-10-07

How to Cite

Urboshi Hazarika, & Samira Behera. (2025). Refinements of Generalized Jacobi Method: A Higher-Order Approach. Science & Technology Journal, 12(2). https://doi.org/10.22232/stj.2024.12.02.18

Issue

Vol. 12 No. 2 (2024): Volume 12, Issue 2, June 2024

Section

Research Articles

Categories

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Copyright (c) 2025 Urboshi Hazarika, Samira Behera

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