fonction d'interpolation avec la méthode de newton in matlab

main.m
% Sample data
x = [1 2 3 4];
y = [3 1 4 2];

% Compute divided difference coefficients
dd = divdiff(x, y);

% Define a function to evaluate the polynomial using divided differences
f = @(x) newton_eval(x, x, dd);

% Compute interpolated values for some new x values
x_new = linspace(0, 5, 101);
y_new = f(x_new);

% Plot original data and interpolated values
plot(x, y, 'o', x_new, y_new);
legend('Data', 'Interpolated');
xlabel('X');
ylabel('Y');

function c = divdiff(x, y)
% Compute divided difference coefficients
    n = length(x);
    c = y;

    for j = 2:n
        for i = n:-1:j
            c(i) = (c(i) - c(i-1)) / (x(i) - x(i-j+1));
        end
    end
end

function y = newton_eval(x, xk, c)
% Evaluate interpolating polynomial using divided differences
    n = length(xk);
    y = c(n);

    for i = n-1:-1:1
        y = c(i) + (x - xk(i)) .* y;
    end
end
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