Pixel matrices: An elementary technique for solving nonlinear systems

TL;DR

This paper introduces a novel pixel matrix method for approximating the entire solution set of nonlinear systems by visualizing functions as pixel matrices and applying matrix operations.

Contribution

It presents a new graphical technique that uses pixel matrices and matrix operations to approximate solutions of nonlinear systems, offering a visual and systematic approach.

Findings

Effectively visualizes solution sets for nonlinear systems.

Provides a systematic matrix-based approximation method.

Applicable to algebraic, smooth, and continuous functions.

Abstract

A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot each function as a pixel matrix, and to then perform a sequence of basic matrix operations, as dictated by how variables are shared by the relations in the system. The result is a pixel matrix graphing the approximated simultaneous solution set for the system.