Add NewtonRaphsonMethodPolynomial in python #76

python/nonlinear-equations/NewtonRaphsonMethodPolynomial.py

@@ -0,0 +1,38 @@
+"""
+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 = polyval(f, x) returns the value of a polynomial evaluated at x;
+y = polyder(f) returns the coefficients of the derivative of the polynomial
+whose coefficients are given by the vector p;
+"""
+
+def newton_raphson_method_polynomial(f, x0, tol, max_iter):
+    def derivative(f, x):
+        h = 10e-10
+        d = (f(x+h) - f(x)) / h
+        return d
+
+    eps = tol
+    for i in range(1, max_iter):
+        fx = f(x0)
+        fxd = derivative(f, 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 = f(xi)
+        # check if xi is a root of the polynomial;
+        if abs(fxi) < eps:
+            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');