NewtonZero never comes down
- To: mathgroup at smc.vnet.net
- Subject: [mg51416] NewtonZero never comes down
- From: Roger Bagula <tftn at earthlink.net>
- Date: Sat, 16 Oct 2004 04:21:07 -0400 (EDT)
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
I've tried several ways to find better values for
zeta zeros fast and easy...
FindRoot just doesn't give much accuracy.
NewtonZero tends to just spin it's wheels on my machine....
Here's what I came up with that gets about 20 places
and pretty fast relatively.
It's much better than FindRoot anyway!
The zeta zeros all seem to be transcendental irrational numbers
and are harder to calculate than most numbers in modern number theory.
(* finding Zeta Zero roots*)
(* using approximation from analyitic continuation on 0<=z<=1 strip
where zeta dosesn't converge*)
(* gives the zeta zeros given in Jahnke-Emde Tables of Functions, Dover*)
(* definition of Newton function*)
(* ten iterations toward the zero*)
(* values starting at the continuation values approximated*)
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL : http://home.earthlink.net/~tftn
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