% generalized fixed point iteration, section 2.2, problem 2 
clear;
format long;
        
N=20;
K = -2/3;
K = -1;
K = -0.25;
K = -0.8;
K = 0;
alpha = K/(K-1) 
x0 = 2.5;
x = x0
for i=1:N
% x = alpha*x + (1-alpha)*(3+x-2*x^2)^.25;               %g1 K=-0.66, N=10 
% x = alpha*x + (1-alpha)*( (x+3-x^4)/2 )^.5;            %g2 K=-1, N=9 
% x = alpha*x + (1-alpha)*( (x+3)/(x^2+2) )^.5;          %g3,K=.0, N=24 
                                                         %g3,K=.25, N=5 
% x = alpha*x + (1-alpha)*(3*x^4+2*x^2+3)/(4*x^3+4*x-1); %g4, N=5 
x = alpha*x + (1-alpha)*(2 + sin(x));                    % p14(a), K=-0.8, N = 8
[i x]
end