Iterative Solutions for Certain Complex Coefficient Linear Systems: Jacobi and Gauss-Seidel Methods

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Kuantum Teknolojileri ve Enformatik Araştırmaları Dergisi
Volume 3, Issue 1
Iterative Solutions for Certain Complex Coefficient Linear Systems: Jacobi and Gauss-Seidel Methods

Iterative Solutions for Certain Complex Coefficient Linear Systems: Jacobi and Gauss-Seidel Methods

Authors : Ahmet Zahid Küçük, Bayram Köse, Bahriye Karaca

Pages : 1-14

Doi:10.70447/ktve.2786

View : 45 | Download : 1

Publication Date : 2025-04-11

Article Type : Research Paper

Abstract :[eng] In this study, the performance of the Jacobi and Gauss-Seidel iteration methods for solving systems of linear equations with complex coefficients is analyzed. The coefficient matrix of the system is transformed into a real coefficient system by separating the real and imaginary parts. The study aims to compare the accuracy and computational efficiency of these methods within the context of selected examples, while also evaluating their convergence behavior. The findings demonstrate that, for the examples considered, the Gauss-Seidel method converges faster and with lower initial errors compared to the Jacobi method.
Keywords : Linear equations systems with complex coefficients, , Jacobi iteration method, Gauss-Seidel iteration method, Complex-Real transform

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