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Newton’s method spirals
( go to the article → https://www.johndcook.com/blog/2021/01/23/newtons-method-spirals/ )
In [1] 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.
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