% Newton's method to solve the nonlinear system of equation
% (x-0.01)^2 + y^2 = 1
% x^2 - (y-0.01)^2 = .25
% in the first quadrant (near (1/4, 1/4) := x_0

clear;
format long e;

x = [.5; .5]

% repeat the following command till convergence (about 9 iterations)

x = x - [ 2*(x(1)-0.01) 8*x(2); 2*x(1) -2*(x(2)-0.01)]\ ...
    [ x(2)^2+4*( x(2)-0.01 )^2-1; x(1)^2-(x(2)-0.01)^2-0.25 ]