[Edu-sig] Halley's Method for nth root of P

[Kirby Urner]

Here's an interesting function that returns the nth root of P.

Usage:

>>> halley(2,2)     # 2nd root of 2
1.41421356237
>>> 2.0**0.5        # check
1.41421356237

>>> halley(7,3)     # 3rd root of 7
1.91293118277
>>> 7.0**(1./3.)    # check
1.91293118277

>>> halley(1000,4)  # 4th root of 1000 (duh)
10.0

Maybe the math module is even using something similar
(or C internally)?

Kirby


# thanks to Domingo G=F3mez Mor=EDn
# http://www.etheron.net/usuarios/dgomez/Roots.htm

def halley(P,n,d=3D10,x=3D1.0):
       # P -- find nth root of this number
       # n -- whole number root
       # d -- level of depth for recursion (default 10)
       # x -- initial value of x (default 1)
	if d>1:	=09
	   newx =3D ((n+1.0)*P*x + (n-1)*(x**(n+1)))/((n-1)*P + (n+1)*x**n)
   	   return halley(P,n,d-1,newx)	  =20
	else:
	   return x




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I was going to wait until Monday, but now prefer to face the week-end with a
clearer
head.

I had written -

>>Fair enough?

I certainly thought so.

But I will take silence as a no in this case.

So I guess I've seen this through to the end. I am proud of at least that.

Guido:

Please remove the EDU-SIG link to PyGeo.  It's busted anyway

David Ascher:

Thanks for listening.

To Starship:

Please consider my February something (my e-mail archives don't go back far
enough to pinpoint)
request for a crew account, delivered according to instructions, in good
order with receipt acknowledged
- withdrawn.

To Stephen:

I'll settle for the consolation prize.  $300, I believe. You have the
address.

To Kirby:

Love to hear Urner on the Transcendentalists.  Will be checking your site.