1. Nov 13, 2014

### 582153236

1. The problem statement, all variables and given/known data
The Newton iteration formula is based on a Taylor series expansion of the function f(x) around an estimate of the root xn, truncated after the linear term. You are asked to derive a more accurate iteration scheme as follows: Start from the Taylor series expansion of f(x) around xn, and truncate it after the quadratic term; derive then a general iteration formula for xn+1, and explain how you would use it.

2. Relevant equations
Newton's method equation:

Taylor's series expansion with ε=x-x0

3. The attempt at a solution
If you truncate all the terms after the linear term, it becomes a matter of simple rearrangement to isolate xn+1.

However, when truncating after quadratic term, isolating xn+1 becomes considerably more messy. My question is whether it would be valid to try to isolate xn+1. I have considered using quadratic equation but given the tediousness of this approach I am hoping for a different method.

2. Nov 13, 2014

### Dr.D

Sounds like you need to quit dodging the work and go to it.