7. (Exercise 2.3.13 from textbook) Consider solving f(x) = 0 by applying the fixed point iteration method to f(x) ƒ"(x)

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7 Exercise 2 3 13 From Textbook Consider Solving F X 0 By Applying The Fixed Point Iteration Method To F X F X 1 (144 KiB) Viewed 68 times

7. (Exercise 2.3.13 from textbook) Consider solving f(x) = 0 by applying the fixed point iteration method to f(x) ƒ"(x) [ f(x) f'(x) 2f'(x) f'(x) (a) Show that if x is a root of f(x) (i.e. f(x) = 0) then x is a fixed point of g(x) (i.e. g(x) = x+)). (b) Expand our analysis of Newton's method to show this method generally yields cubic convergence. g(x) = 2 = X