function newton_v_fixedpoint;
% p is the approximatoin of newtons's method
% q is the approximation of fixed point method
p=1; q=1;
% n is the number of iterations
n=6;
% the same loop is for the both methods
fprintf(1, '\n \n Compare the two methods \n');
for i=1:1:20
p=p-f(p)/der_f(p);    
q=g(q);
fprintf(1,'Iteration: %3i Newton`s: %12.10f Fixed point: %12.10f \n', i,p,q);
end


function y=g(x);
% use example 2.2#7, solve as fixed point problem 
%y=pi+0.5*sin(x/2);
y=-x^2+x;
%

function y=f(x);
% use example 2.2#7 solve as root finding problem by Newton's method
%y=pi+0.5*sin(x/2)-x;
%y=x^2;
y=(abs(x))^(2/3);


function y=der_f(x);
% use example 2.2#7 solve as root finding problem by Newton's method
%y=cos(x/2)/4-1;
%y=2*x;
y=sign(x)*(abs(x))^(-1/3)*2/3;