generating polynomial using newton divided difference

Hi good day y'all, i'm making a code for newton divided difference but i'm having a hard time generating the right polynomial, can someone please help me? thank you so much.

y=[1 2 3 4];
x=[4.4 4.3 2 5];

n=size(x,2);
DD=zeros(n,n);
DD(:,1)=y';
for j=2:n
    for i=1:(n-j+1)
        num=DD(i+1,j-1)-DD(i,j-1);
        den = (x(i+j-1)-x(i));
        DD(i,j)=num./den;
    end
end
array2table(DD)

ans = 4×4 table
    DD1      DD2         DD3       DD4  
    ___    ________    _______    ______

     1          -10    -3.9855    8.4714
     2     -0.43478     1.0973         0
     3      0.33333          0         0
     4            0          0         0

n=length(x);
a(1)=x(1);
for k=1:n-1
   d(k,1)=(y(k+1)-y(k))/(x(k+1)-x(k));
end
for j=2:n-1
   for k=1:n-j
      d(k,j)=(d(k+1,j-1)-d(k,j-1))/(x(k+j)-x(k));
   end
end
%
for j=2:n
   a(j)=d(1,j-1);
end
yn=vpa(x);
d=vpa(d);
a=vpa(a);
clear x
syms x
%
Df(1)=vpa(1);
c(1)=a(1);
for j=2:n
   Df(j)=(x-yn(j-1)).*Df(j-1);
   c(j)=a(j).*Df(j);
end
format short
f=simplify(sum(c))

f = 

Answer 1

[Vinayak Agrawal]

Hi Michael,

an updated version of your code that computes the polynomial expression using symbolic calculations in MATLAB:

% Given data

y = [1 2 3 4];

x = [4.4 4.3 2 5];

n = length(x);

DD = zeros(n, n);

DD(:, 1) = y';

for j = 2:n

for i = 1:(n-j+1)

num = DD(i+1, j-1) - DD(i, j-1);

den = (x(i+j-1) - x(i));

DD(i, j) = num / den;

end

end

% Coefficients of the polynomial

a = diag(DD)';

yn = sym(x);

d = sym(diag(DD));

% Compute the polynomial expression

syms x;

f = a(1);

for j = 2:n

term = 1;

for k = 1:j-1

term = term * (x - yn(k));

end

f = f + a(j) * term;

end

% Simplify the polynomial expression

f = simplify(f);

disp(f);

In this updated code, try running this. I've used symbolic calculations (sym) to generate the polynomial expression based on the computed coefficients. The resulting polynomial expression is simplified using simplify for a more concise form.

When you run the code, it will display the simplified polynomial expression. You can further customize the output format or manipulate the polynomial expression as needed.

I hope this helps you generate the correct polynomial expression using Newton's divided difference interpolation.

[michael]

thank you for this, but it is the same with my prev works, i get all the terms right except for the constant term

[michael]

finally i got it, thanks again

[Vinayak Agrawal]

no problem michael your attempt was great