Complex Analysis: Explorations with F(Z)

Complimentary software to accompany the text

Complex Analysis: for Mathematics and Engineering

Page 118. Example concerning the roots of the cubic polynomial .
Fixed point iteration with .
The initial point will generate a sequence which converges to

, red,

, yellow,

, blue.

The graph is:

Basins of attraction for Newton's method applied to .

The figures for this example were drawn using the F(Z) example file: 119CP41.fzw

(c) John Mathews, 1998