Pixel matrices: An elementary technique for solving nonlinear systems
This provides a new elementary method for solving nonlinear systems, potentially useful for practitioners needing approximate solutions without advanced numerical methods.
The paper introduces a technique to approximate the entire solution set of nonlinear systems by plotting each function as a pixel matrix and performing matrix operations, yielding a graphical approximation of the simultaneous solution set.
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.