A Comprehensive Error Estimation Framework For Systems Of Linear Equations Via The Banach Contraction Principle

In this paper, we studied an application of the Banach Contraction principle to the presence and singularity of a solution to a linear equation system using the Jacobi iterative approach and the Gauss-Seidel iterative approach. The aim of this paper is to establish the relationship between error estimation terms using the Banach fixed point theorem and actual error. Additionally, the relationship between the obtained results and existing ones is demonstrated through appropriate examples.