Create newtons_method.m

Author: Numerically-Stable

Numerical Methods/NewtonRaphson/newtons_method.m

@@ -0,0 +1,49 @@
+function root = newtons_method(x0, f, f_prime, tolerance, epsilon, max_iterations)
+% NEWTONS_METHOD  Newton–Raphson root-finding algorithm
+% Source: Wikipedia
+%   root = newtons_method(x0, f, f_prime, tolerance, epsilon, max_iterations)
+%
+%   Inputs:
+%       x0              - Initial guess for the root
+%       f               - Function handle whose root we want to find
+%       f_prime         - Derivative of the function (function handle)
+%       tolerance       - Stop if successive estimates differ by less than this
+%       epsilon         - Avoid division if derivative magnitude < epsilon
+%       max_iterations  - Maximum allowed number of iterations
+%
+%   Output:
+%       root            - Approximate root (or NaN if not converged)
+
+root = NaN;  % Default return value if not converged
+
+for k = 1:max_iterations
+    y = f(x0);
+    yprime = f_prime(x0);
+
+    % Avoid division by very small derivative
+    if abs(yprime) < epsilon
+        fprintf('Derivative too small. Stopping at iteration %d.\n', k);
+        return
+    end
+
+    % Newton update
+    x1 = x0 - y / yprime;
+
+    % Check for convergence
+    if abs(x1 - x0) <= tolerance
+        root = x1;
+        fprintf('Iter %d \n x = %d .\n', k,x1);
+        fprintf('Converged after %d iterations.\n', k);
+        return
+    end
+
+    % Prepare for next iteration
+    x0 = x1;
+
+    % Display current step values
+    fprintf('Iter %d \n x = %d \n', k,x0);
+end
+
+fprintf('Did not converge within %d iterations.\n', max_iterations);
+
+end