newton method ang gamma in matlab

To use Newton's Method to find the root of the gamma function in Matlab:

main.m
% Define the function and its derivative
f = @(x) gamma(x);
fp = @(x) psi(x).*gamma(x);

% Set a starting point
x0 = 2;

% Set the tolerance and maximum number of iterations
tol = 1e-10;
maxit = 1000;

% Iterate using Newton's method
x = x0;
for i = 1:maxit
    fx = f(x);
    fpx = fp(x);
    if abs(fx) < tol
        break
    end
    x = x - fx/fpx;
end

% Print the result
fprintf('The root of gamma function is: %f\n', x);
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In the code above, we defined the gamma function and its derivative using anonymous functions, set a starting point, and defined the tolerance and maximum number of iterations. Then, we iteratively applied Newton's method to find the root of gamma function.

Note that the gamma function can have multiple roots, and the starting point can critically affect the convergence of Newton's method. Therefore, it is important to choose a good starting point and perform a sensitivity analysis to test the robustness of the algorithm.