So I've written a function in MATLAB which solves a non-linear system of equation:
$f(x,y) = 0$
$g(x,y) = 0$
for two variables.
I am now tasked with finding a stationary point (critical point) for a function f(x,y) using my newton method program.
How is this supposed to work? How is the newton method helpful with finding criticals points? I can't really see how to apply this.
I should also add, that for this specific problem I am given the function:
$f(x,y)= (x-1)^2 + (y-1)^2$
Since my function for the Newton method relies on two functions f & g as input arguments.
Should I then treat any function f as a two functions?
i.e:
$f(x,y)= (x-1)^2$ and $g(x,y)= (y-1)^2$?