Summary: SYSTEMS OF NONLINEAR EQUATIONS
Widely used in the mathematical modeling of real world
We introduce some numerical methods for their solution.
For better intuition, we examine systems of two nonlinear
equations and numerical methods for their solution. We
then generalize to systems of an arbitrary order.
The Problem: Consider solving a system of two nonlin-
f(x; y) = 0
g(x; y) = 0 (1)
Example: Consider solving the system
f(x; y) x2 + 4y2 9 = 0
g(x; y) 18y 14x2 + 45 = 0
A graph of z = f(x; y) is given in Figure 1, along with
the curve for f(x; y) = 0.
Figure 1: Graph of z = x2 + 4y2 9, along with z = 0
on that surface
To visualize the points (x; y) that satisfy simultaneously