%% FPI Example

%% Example 1:  Solve cos(x)=x, with FPI and initial point x_0=5.

echo on

f=inline('cos(x)');
x0=5;
NumIters=15;

xc=fpi2(f,x0,NumIters);

%Consider |f(x)-f(y)| over |x-y| (Think:  MVT)
k=NumIters+1;
G=(xc(3:k)-xc(2:k-1))./(xc(2:k-1)-xc(1:k-2));
G'
-sin(xc(end))


pause

%% Example 2: Run FPI for the following functions g, x_0=1/2

g1=inline('1-x.^3');
g2=inline('(1-x).^(1/3)');
g3=inline('(1+2*x.^3)./(3*x.^2+1)');

x0=0.5;
NumIters=25;
x1=fpi2(g1,x0,NumIters);
x2=fpi2(g2,x0,NumIters);
x3=fpi2(g3,x0,NumIters);

echo off