Question

i want to verify that when newton's method is used to compute sqrt(R) (by solving the equation x^2=R), the sequence o iterates is defined by

x_(n+1)=.5(x_(n) + (R/x_(n))

Answer 1

f(x) = Xn^2 - R
f'(x) = 2Xn
Xn+1 = Xn - f(Xn)/f'(Xn)
Xn+1 = Xn - (Xn^2-R)/2Xn
Xn+1 = 2Xn^2/2Xn - Xn^2/2Xn + R/2Xn
Xn+1 = Xn/2 +R/2Xn

Answer 2

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THANKS AGAIN.

Answer 3

I am not around much. Do not want email or anything. I am happy to help if I am free to do so but am usually building boats outside.