Newton’s method spirals
( go to the article → https://www.johndcook.com/blog/2021/01/23/newtons-method-spirals/ )
In  the authors look at applying Newton’s root-finding method to the function f(z) = zp where p = a + bi. They show that if you start Newton’s method at z = 1, the kth iterate will be (1 – 1/p)k. This converges when a > 1/2, runs around in circles when a = […] The post Newton’s method spirals first appeared on John D. Cook.
Jan. 23, 2021, 6:42 p.m.