(3.4) Cubic spline (natural): MatLab code + download link.

Code's download link:
https://drive.google.com/file/d/1-yVLmzQbrgXEUNtmwWD2xvBKtsSde0h0/view?usp=sharing

Alternatively, you can copy and paste from below:
% Natural cubic spline interpolation
% Find the approximate value of f(1.5) from
% (x,y)= (0,1), (1,e), (2,e^2) & (3,e^3).

n = input('Enter n for (n+1) nodes, n: ');
x = zeros(1,n+1);
a = zeros(1,n+1);

for i = 0:n
fprintf('Enter x(%d) and f(x(%d)) on separate lines: \n', i, i);
x(i+1) = input(' ');
a(i+1) = input(' ');
end


m = n - 1;
h = zeros(1,m+1);
for i = 0:m
h(i+1) = x(i+2) - x(i+1);
end

xa = zeros(1,m+1);
for i = 1:m
xa(i+1) = 3.0*(a(i+2)*h(i)-a(i+1)*(x(i+2)-x(i))+a(i)*h(i+1))/(h(i+1)*h(i));
end

xl = zeros(1,n+1);
xu = zeros(1,n+1);
xz = zeros(1,n+1);
xl(1) = 1;
xu(1) = 0;
xz(1) = 0;

for i = 1:m
xl(i+1) = 2*(x(i+2)-x(i))-h(i)*xu(i);
xu(i+1) = h(i+1)/xl(i+1);
xz(i+1) = (xa(i+1)-h(i)*xz(i))/xl(i+1);
end

xl(n+1) = 1;
xz(n+1) = 0;
b = zeros(1,n+1);
c = zeros(1,n+1);
d = zeros(1,n+1);
c(n+1) = xz(n+1);

for i = 0:m
j = m-i;
c(j+1) = xz(j+1)-xu(j+1)*c(j+2);
b(j+1) = (a(j+2)-a(j+1))/h(j+1) - h(j+1) * (c(j+2) + 2.0 * c(j+1)) / 3.0;
d(j+1) = (c(j+2) - c(j+1)) / (3.0 * h(j+1));
end

fprintf('\nThe numbers x(0), ..., x(n) are:\n');
for i = 0:n
fprintf(' %5.4f', x(i+1));
end

fprintf('\n\nThe coefficients of the spline on the subintervals are:\n');
fprintf(' a(i) b(i) c(i) d(i)\n');
for i = 0:m
fprintf('%11.8f %11.8f %11.8f %11.8f \n',a(i+1),b(i+1),c(i+1),d(i+1));
end

Видео (3.4) Cubic spline (natural): MatLab code + download link. канала 3one4