% Construct the table for exp(x) using quadratic interp
% Note that nodes(1) is 0, nodes(2) = h, nodes(3) = 2*h
% since subscripts begin at 1 in matlab

h = 0.01
nodes = 0:h:1;
expTable = exp(nodes);

% Specify a value x between nodes
% and determine which linear segment it is in

x = 0.51515
k = floor( (x-0) / h)
if k >= 99
   k = 98;
end

x0 = nodes(k+1) % this is node k
y0 = expTable(k+1)

x1 = nodes(k+2) % this is node k + 1
y1 = expTable(k+2)

x2 = nodes(k+3) % this is node k + 2
y2 = expTable(k+3)

% interpolated value xi is

yi =   y0*(x-x1)*(x-x2) / ((x0-x1)*(x0-x2)) ...
     + y1*(x-x0)*(x-x2) / ((x1-x0)*(x1-x2)) ...
     + y2*(x-x0)*(x-x1) / ((x2-x0)*(x2-x1))

% Interpolation error is

err = yi - exp(x)