1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Quadratic Newton's Method

  1. Nov 13, 2014 #1
    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. jcsd
  3. Nov 13, 2014 #2
    Sounds like you need to quit dodging the work and go to it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted