Complex Analysis: Theory and Applications · Problem 4.2.3

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · newtons-method-degree-one

Problem

Prove that Newton's method always works for polynomials having degree 1 (functions of the form f(z)=az+bf(z) = az + b, where a≠0a \neq 0). How many iterations are necessary before Newton's method produces the solution z=−baz = -\dfrac{b}{a} to f(z)=0f(z) = 0?

Browse the problem library