aitkenneville.m

Interpolation routines in matlab

%
% Aitken Neville algorithm to compute the value
% of the interpolating polynomial at a given point.
%
% function [p] = AitkenNeville( x, f, z )
%
% input:
%        x:     vector containing the 
%               interpolation points
%        f:     vector containing the values 
%               to be interpolated
%        z:     vector of points at which the 
%               interpolating polynomial has to be evaluated
%
% output:
%        p:     vector with values of the interpolating polynomial
%
%

function [p] = AitkenNeville( x, f, z );


n = size(x(:),1);


if size(f(:),1) ~= n 
   ifail = 1;
   return
end

m = size(z(:),1);

for k = 1:m
    P = zeros(n,n);

    P(1:n,1) = f(:);

    for j = 2:n
        for i = j:n
            P(i,j) = P(i-1,j-1) + (z(k) - x(i-j+1)) / (x(i) - x(i-j+1)) * ( P(i,j-1) - P(i-1,j-1) );
        end
    end

    p(k) = P(n,n);
end

Aitken_Neville(:,1) = x(:);
Aitken_Neville(:,2:n+1) = P;
disp('        x         f  ')
disp(Aitken_Neville)