From 2765f4932063bf61c061f5736c9ac06cf9d4b0b6 Mon Sep 17 00:00:00 2001
From: Basil Feitknecht <114588139+bfeitknecht@users.noreply.github.com>
Date: Sun, 18 Jan 2026 14:30:02 +0100
Subject: [PATCH] Fix Newton's Method

The old one incorrectly uses the absolute value of the derivative
---
 semester3/numcs/parts/03_zeros/04_newton-one-d.tex | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/semester3/numcs/parts/03_zeros/04_newton-one-d.tex b/semester3/numcs/parts/03_zeros/04_newton-one-d.tex
index 208c701..712e7cb 100644
--- a/semester3/numcs/parts/03_zeros/04_newton-one-d.tex
+++ b/semester3/numcs/parts/03_zeros/04_newton-one-d.tex
@@ -23,9 +23,12 @@ falls $F(x^*) = 0$ und $F^(x^*) \neq 0$
 \begin{code}{python}
 def newton_method(f, df, x: float, tol=1e-12, maxIter=100):
     """ Use Newton's method to find zeros, requires derivative of f """
-    iter = 0
-    while (np.abs(df(x)) > tol and iter < maxIter):
-        x -= f(x)/df(x); iter += 1
+    k = 0
+    fx = f(x)
+    dfx = df(x)
+    while (np.abs(fx) > tol and k < maxIter):
+        x -= fx / dfx
+        k += 1
     
-    return x, iter
+    return x, k
 \end{code}