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Question: iterative method convergence

Question:iterative method convergence

GPY 80 Maple
linear rootfinding homework convergence cubic
February 01 2015
1

I've got a function f(x_n) = (x_n-1)^3

and need to show that for the iterative method

x_(n+1)= x_n - f(x_n)/(sqrt(f'(x_n)^2-f(x_n)*f''(x_n), at a simple root we have cubic convergence while at a multiple root, it converges linearly.

I understand that the approach is to write either a recursive function or a sequence, but i'm confused about the structure since both x and n are being incremented

 
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