%Program 1.2 Fixed-Point Iteration
%Computes approximate solution of f(x)=x
%Input: function f, initial guess x0, and  
%       number of steps k
%Output: Approximate solution xc and err=|x(k+1)-xk|
function [xc,err]=fpi(f,x0,k)
x(1)=x0;
for s=1:k
  x(s+1)=f(x(s));
end
xc=x(k+1);
err=f(xc)-xc;
___________________________________________________________________________

clear;
format long
f=inline('1+x-x.^2/4');
A=zeros(8,2);
for i=1:8;
[x,y]=fpi(f,1.6,j);
A(j,1)=x;
A(j,2)=y;
end
disp(' ')    %  a blank line
disp(' n         pn                        |f(pn)-pn| ')
disp('------------------------------------------------------')
for k=1:8
  disp(sprintf('%2.0f    %7.15e    %7.15e ',k,A(k,1),A(k,2)))
end
 
 n         pn                        |f(pn)-pn| 
------------------------------------------------------
 1    1.960000000000000e+000    3.960000000000008e-002 
 2    1.999600000000000e+000    3.999599999999770e-004 
 3    1.999999960000000e+000    3.999999975690116e-008 
 4    2.000000000000000e+000    2.220446049250313e-016 
 5    2.000000000000000e+000    0.000000000000000e+000 
 6    2.000000000000000e+000    0.000000000000000e+000 
 7    2.000000000000000e+000    0.000000000000000e+000 
 8    2.000000000000000e+000    0.000000000000000e+000 
% If we try to find p=-2, then it diverges 
clear;
format long
f=inline('1+x-x.^2/4');
A=zeros(15,2);
for j=1:15;
[x,y]=fpi(f,-2.01,j);
A(j,1)=x;
A(j,2)=y;
end
disp(' ')    %  a blank line
disp(' n         pn                        |f(pn)-pn| ')
disp('------------------------------------------------------')
for k=1:15
  disp(sprintf('%2.0f    %7.15e    %7.15e ',k,A(k,1),A(k,2)))
end
 
 n         pn                        |f(pn)-pn| 
------------------------------------------------------
 1    -2.020025000000000e+000    -2.012525015624966e-002 
 2    -2.040150250156249e+000    -4.055326080315158e-002 
 3    -2.080703510959401e+000    -8.233177512969458e-002 
 4    -2.163035286089095e+000    -1.696804122166338e-001 
 5    -2.332715698305729e+000    -3.603906322804962e-001 
 6    -2.693106330586225e+000    -8.132054269609008e-001 
 7    -3.506311757547126e+000    -2.073555535278304e+000 
 8    -5.579867292825430e+000    -6.783729751385748e+000 
 9    -1.236359704421118e+001    -3.721463296790684e+001 
10    -4.957823001211801e+001    -6.135002227836199e+002 
11    -6.630784527957378e+002    -1.099172586404974e+005 
12    -1.105803370932931e+005    -3.057002736916584e+009 
13    -3.057113317253677e+009    -2.336485458632446e+018 
14    -2.336485461689559e+018    -1.364791078171668e+036 
15    -1.364791078171668e+036    -4.656636717642458e+071