Create NewtonZeroFinder.py

Function to search the roots of a differentiable function with the Newton's method.

Author: servindc

Mathematical_Algorithms/src/NewtonZeroFinder.py

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+def find_zero_Newton(f,x0=1,df=None,dx=0.1,iterations=1000,precision=1e-7,epsilon=1e-15):
+    """
+        Uses Newton's method to find a root near the given point x0.
+    """
+	if df==None:    # Aproximates the derivative if missing
+		def derivative(x):
+			return (f(x+dx)-f(x))/dx
+		df = derivative
+	sol = False
+	for i in range(iterations):
+		y, dy = f(x0), df(x0)
+		if abs(dy) < epsilon: break
+		
+		x1 = x0 - y/dy
+		if abs(x1 - x0) <= precision*abs(x1):
+			sol = True
+			break
+		x0 = x1
+	if sol:
+		print("Solution FOUND")
+		return x1
+	print("Solution NOT FOUND")