NewtonRaphson

python/NewtonRaphson.py

@@ -0,0 +1,30 @@
+import numpy as np
+
+
+def NewtonRaphson(f, x0, tol, max_iter):
+    # solves f(x) = 0 by doing max_iter steps;
+    # the method requires one initial value (x0)
+    # which should be chosen close to the root;
+    # y = np.polyval(f, x) returns the value of a polynomial evaluated at x;
+    # y = np.polyder(f) returns the coefficients of the derivative of the polynomial
+    # whose coefficients are given by the vector p;
+    fd = np.polyder(f)
+    for i in range(0, max_iter):
+        fx = np.polyval(f, x0)
+        fxd = np.polyval(fd, x0)
+        # calculate the value of the new approximation, xi, using the formula;
+        xi = x0 - fx / fxd
+        # calculate the value of the polynomial evaluated at xi;
+        fxi = np.polyval(f, xi)
+        # check if xi is a root of the polynomial;
+        if abs(fxi) < np.spacing(1):
+            x = xi
+            return [x, i]
+        epsilon = abs((xi - x0) / xi)
+        # stop if the method reached its convergence limit;
+        if epsilon < tol:
+            x = xi
+            return [x, i]
+        # update the last computed value;
+        x0 = xi
+    print("Maximum number of iterations reached")