Hello. I've been approached with a problem of explaining why Newton Raphson method fails for some functions. I came across a book in Numerical Analysis (Kellison's book) that the method may fail if(adsbygoogle = window.adsbygoogle || []).push({});

1.) f'(x)=0

2.) The initial value is taken at a maximum or minumum point,

3.) The initial value is taken at a point of inflection,

4.) The initial value is taken near a maximum point and a minimum point,

5.) The initial value is taken near a point of inflection.

Now I can explain (1). Newton's Method will fail since the iteration is given by

[itex]

x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

[/itex]

Therefore making the whole thing undefined.

As for (2), since minima and maxima have f'(x)=0, they will fail for the same reasons as (1)

As for (3), ... I'm totally clueless. I dont know how a point of inflection (f''(x)=0) could be related to the Iteration that uses f'

As for (4), I also know that choosing near a minima or maxima might make the method "oscillate", but what I'm looking for are more concrete answers; something that can be related to f'(x) or something that resembles a proof.

As for (5), I have no idea why it may fail for an initial value near a point of inflection..

All help is appreciated,

reli~

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: When Newton Raphson Fails

**Physics Forums | Science Articles, Homework Help, Discussion**