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.
