WOLFRAM|DEMONSTRATIONS PROJECT

Newton's Method on a Mesh of Initial Guesses

​
c
3
1.2
c
2
1.76
c
1
-3.22
c
0
-5
featured initial guess
0
0 iterates to 1.66049
This Demonstration shows the path of 50 iterations of Newton's method from a mesh of starting points attempting to solve the cubic equation
c
3
3
x
+
c
2
2
x
+
c
1
x+
c
0
=0
. A "featured" initial guess is highlighted in blue. If the absolute value of
f'(x)
is less than
-5
10
, no iteration is taken.