quadratic lagrange interpolation in matlab

main.m
% Define function to be interpolated
f = @(x) sin(x);

% Define interpolation points
x_interp = [-1, 0, 1];

% Compute Lagrange basis polynomials and weights
l0 = @(x) (x-x_interp(2))*(x-x_interp(3))/((x_interp(1)-x_interp(2))*(x_interp(1)-x_interp(3)));
l1 = @(x) (x-x_interp(1))*(x-x_interp(3))/((x_interp(2)-x_interp(1))*(x_interp(2)-x_interp(3)));
l2 = @(x) (x-x_interp(1))*(x-x_interp(2))/((x_interp(3)-x_interp(1))*(x_interp(3)-x_interp(2)));
w0 = f(x_interp(1))/(l0(x_interp(1))*(x_interp(1)-x_interp(2))*(x_interp(1)-x_interp(3)));
w1 = f(x_interp(2))/(l1(x_interp(2))*(x_interp(2)-x_interp(1))*(x_interp(2)-x_interp(3)));
w2 = f(x_interp(3))/(l2(x_interp(3))*(x_interp(3)-x_interp(1))*(x_interp(3)-x_interp(2)));

% Define points at which to interpolate
x_vals = linspace(-2,2,101);

% Compute interpolated function values
y_vals = w0*l0(x_vals) + w1*l1(x_vals) + w2*l2(x_vals);

% Plot original function and interpolated function
plot(x_vals, f(x_vals));
hold on;
plot(x_vals, y_vals);
legend('Original function', 'Interpolated function');
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