Error in Hermite Polynomial

Hermite_Polynomial.m

function Q = Hermite_Polynomial(X, Y, YP)

n = length(X) - 1;

Q = zeros(2*n + 2, 2*n + 2);

for i = 0:n

z(2*i + 1) = X(i + 1);

z(2*i + 2) = X(i + 1);

Q(2*i + 1, 1) = Y(i + 1);

Q(2*i + 2, 1) = Y(i + 1);

Q(2*i + 2, 2) = YP(i + 1);

if i ~= 0

Q(2*i + 1, 2) = (Q(2*i + 1, 1) - Q(2*i - 1, 1)) / (z(2*i + 1) - z(2*i - 1));

end

end

for i = 2:2*n + 1

for j = 2:i

Q(i, j) = (Q(i, j - 1) - Q(i - 1, j - 1)) / (z(i) - z(i - j + 1));

end

end

result = Q(i,j);

end

main.m

clear all

X = [1, 2, 3];

Y = [1.105170918, 1.491824698, 2.459603111];

YP = [0.2210341836, 0.5967298792, 1.475761867];

x_interp = 1.25;

% Compute divided differences

Q = Hermite_Polynomial(X, Y, YP);

% Interpolate using Hermite polynomial

n = length(X) - 1;

result_H5 = Q(1, 1);

for i = 1:2*n+1

Q_ii = Q(i,i);

product = 1;

for j = 0:i-1

Q_ii = Q_ii * (x_interp - X(j));

end

result_H5 = result_H5 + Q_ii;

end

% Compute Hermite interpolation using H3(1.25)

result_H3 = Q(1, 1);

for i = 1:2*n-1

Q_ii = Q(i,i);

product = 1;

for j = 0:i-1

product = product * (x_interp - X(j));

end

result_H3 = result_H3 + Q_ii;

end

% Display results

disp(['H5(1.25) approximation: ', num2str(result_H5)]);

disp(['H3(1.25) approximation: ', num2str(result_H3)]);

The above is my code when I run it I get the error saying the following:

Array indices must be positive integers or logical values.

Error in main (line 15)

z_product = z_product * (x_interp - X(j);

Array indices must be positive integers or logical values.

Error in main (line 29)

product = product .* (x_interp - X(j));

Please help me debug the it

Answer 1

[Alan Stevens]

In line

for j = 0:i-1

you have j starting at zero. Matlab's indices start at 1, so the following line should have X(j+1) not X(j).