Newton interpolation for 9 values

Hello im trying to run an interpolation for the values shown below in the code but for a reason when i plot the results I get a curve that doesnt go through all the points. Can someone help me solve this problem plz?

X=[0 14 36 52 68 75 83 94 100];   %  time (sec)
Y=[6000 5750 4530 3675 1762 1279 895 429 151];  % Range (meters)
  
n = length(X)         % set n = 9
h = X(2)-X(1);       % stepsize
d = zeros(n,n)        % 9x9 matrix of zeros
d(:,1)= Y             % 
for j = 2:n
    for i=j:n
        d(i,j) = d(i,j-1)-d(i-1,j-1)
    end
end
 
C = d(n,n);
for k = n-1:-1:1
    p = poly(X(1))/h;
    p(2) = p(2)-(k-1);
    C = conv(C,p)/k;
    m = length(C);
    C(m) = C(m)+d(k,k);
end
  
A = polyval(C,n)
t = linspace(X(1),X(n),100)
y = polyval(C,t)
 
set(figure(1),'DefaultLineLineWidth',1.5)
plot(t,y,'b')
hold on 
plot(X,Y,'ro')

Thank you !

[Asad (Mehrzad) Khoddam]

Because the time step is not constant, you should use divided difference not differences

[Evangelos Rompogiannakis]

Could you please give a hint on how to implement this in my code. I used the difference of X(1) and X(2).

Answer 1

[Monisha Nalluru]

Inorder to use divided difference in newton interpolation in the code

Refer the the corresponding x according to formula

As an example

for j = 2:n
    for i=j:n
        d(i,j) = (d(i,j-1)-d(i-1,j-1))/(X(i)-X(i-j+1));
    end
end

Also refer the code from file example which can give you idea on iimplementation:

https://www.mathworks.com/matlabcentral/fileexchange?q=newton+interpolation