% Section 3.1, problem 6(a)

format long
x=[ 0    0.25    0.5     0.75];
z=[ 1 1.64872 2.71828 4.48169];
xstar = 0.43;

n = length(x)-1;

for j = 1:n
  for i = n:-1:j
    z(i+1) = ( (xstar-x(i-j+1))*z(i+1) - (xstar-x(i+1))*z(i) ) ...
                /( x(i+1)-x(i-j+1) ) ;
  end
end        

z(n+1)