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newton-raphson failure case

I know its a bit random, but does anyone have an example of a failure case for the newton-raphson method of calculating roots of equations? I need one for my cwk, but my graphical calc's started playing up and i've bin trying to find one for about an hour! Thanks!
Reply 1
Avatar for JohnSPals
JohnSPals
JML161
I know its a bit random, but does anyone have an example of a failure case for the newton-raphson method of calculating roots of equations? I need one for my cwk, but my graphical calc's started playing up and i've bin trying to find one for about an hour! Thanks!


How about where the gradient at the point in question (i.e. dy/dx) = 0? Because then the tangent won't intercept the x-axis, which is required for the N-R method to work.

:smile:
Reply 2
Avatar for JML161
JML161
OP
1
GENIUS! Just need to find a line that does that...
Thanks muchly :smile:

... now to get that damned calculator to work! :frown:
Reply 3
Avatar for JohnSPals
JohnSPals
JML161
GENIUS! Just need to find a line that does that...
Thanks muchly :smile:

... now to get that damned calculator to work! :frown:


Well that's easy enough. Just find a turning point or point of inflection. That's some of the easy Pure stuff you'll get :smile:
Reply 4
Avatar for Aitch
Aitch
2
JML161
I know its a bit random, but does anyone have an example of a failure case for the newton-raphson method of calculating roots of equations? I need one for my cwk, but my graphical calc's started playing up and i've bin trying to find one for about an hour! Thanks!


Try the attached part (c)

It does just what you want!

Aitch
nrfail.doc76.3KB
JohnSPals
Well that's easy enough. Just find a turning point or point of inflection. That's some of the easy Pure stuff you'll get :smile:


for my failure can my equation have a fraction eg - 3/4 x^2
Reply 6
Avatar for JohnSPals
JohnSPals
darth_vader05
for my failure can my equation have a fraction eg - 3/4 x^2


Sure. Imagine this curve - a maximum will be at (0,0) hence it fails at x=0.

Differentiating: d [-0.75x2]/dx = -1.5x

At turning point, d [-0.75x2]/dx = -1.5x = 0
Therefore x = 0
Therefore y = 0 when substituting into the equation of the curve
Reply 7
Avatar for Fly.
Fly.
1
The newton raphson method will break down for f(x) at a if

f(a)/f'(a)+f(a-f(a)/f'(a))/f'(a-f(a)/f'(a))=0
Reply 8
Avatar for Aitch
Aitch
2
Here's another example from an old Edexcel paper, if you need one:

Aitch
nrfail2.doc18.9KB

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