Iteration Procedure for the N-Dimensional System of Linear Equations

TL;DR

This paper introduces a geometrically interpreted iterative method for solving N-dimensional linear systems, demonstrating convergence and illustrating its application with a numerical example.

Contribution

It presents a new simple iteration technique for linear equations based on geometric interpretation, with proven convergence.

Findings

Method converges for certain classes of linear systems

Provides a visual and geometric understanding of the iteration process

Includes a numerical example demonstrating effectiveness

Abstract

A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method is obtained and a simple numerical example is provided.