Here's a simple example for you to follow:
% Functions
f = @(x,y) x^2 + y - 5.94; % i.e. the equation is x^2+y=5.94
g = @(x,y) x + y^2 - 3.41; % similarly this represents equation x+y^2=3.41
F = @(x,y)[f(x,y); g(x,y)];
% Jacobian
% J = [df/dx, df/dy;
% dg/dx, dg/dy];
J = @(x,y) [2*x 1; 1 2*y];
% Initial guess
xy = [1; 1];
% Tolerance
tol = 10^-6;
err = 1;
while err>tol
xynew = xy - J(xy(1),xy(2))\F(xy(1),xy(2));
err = abs(xynew-xy);
xy = xynew;
end
disp(xy)
