interpoler une fonction methode de tchebyshev in matlab

main.m
% Define the function to interpolate
f = @(x) 1./(1+25*x.^2);

% Define the Tchebyshev points
N = 5;
x = cos((0:N)*pi/N);

% Compute the Tchebyshev coefficients
c = zeros(1,N+1);
for k = 0:N
    c(k+1) = ((-1)^k)*sum(f(x).*cos(k*acos(x)));
end

% Evaluate the function using the Tchebyshev interpolation
x_eval = -1:0.01:1;
p = zeros(size(x_eval));
for k = 0:N
    p = p + c(k+1)*cos(k*acos(x_eval));
end

% Plot the original function and its Tchebyshev interpolation
figure;
plot(x_eval, f(x_eval), 'LineWidth', 2);
hold on;
stem(x, f(x), 'filled');
plot(x_eval, p, '--', 'LineWidth', 2);
legend('Original Function', 'Tchebyshev Points', 'Tchebyshev Interpolation');
title('Tchebyshev Interpolation for a Given Function');
xlabel('x');
ylabel('y');
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