% newtdriver.m

% This is a driver which constructs the vector of
% abscissas and the vector of ordinates for use in the
% newtpoly.m function.

% Construct the vectors
nodes = [0;1;2;3;4];            
                              % Nodes for interpolating polynomial
fvals = cos(nodes);         
                              % Function values for the interpolating
                              % polynomial
x     = [0:0.01:4]';          % x-values where we plan to evaluate the
                              % interpolating polynomial.
% Calling newtpoly.m to retrieve the 
% polynomial coefficients the 
% Divided Difference Table.
% NOTE: delete the semicolon if you want
% to see the output;
[coefs,DT] = newtpoly(nodes,fvals);


% Calling nestmult.m to evaluate the interpolating polynomial
% at the points contained in the vector x.
a = diag(DT);                   % Initializing the coefficients of the
                                % Newton interpolating polynomial

% Calling the nested multiplication routine in nestmult.m   
% NOTE: delete the semicolon if you want
% to see the output;
 out = nestmult(a,nodes,x);

plot(x,out,nodes,fvals,'g*');