Re: What is the greatest known Fibonacci number?
- To: mathgroup at smc.vnet.net
- Subject: [mg16719] Re: What is the greatest known Fibonacci number?
- From: Peter W <pewei at algonet.se>
- Date: Wed, 24 Mar 1999 02:23:41 -0500
- Organization: Telenordia
- References: <7c5a5k$7op@smc.vnet.net> <7cq3oj$54i@smc.vnet.net> <7ct4it$870@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I have found my implicit formula it is something like this:
ss=sqrt[5]
q[n]=1/ss ( ((ss+1)/2)^(n+1) - ((1-ss)/2)^(n+1) )
q[100000]//N//Timing I get:
({0. Second, 4.202692703 10^20898})
Try it You will like it!
I hope I got the paratezizs right
The idea is to diagonalize Vesa-Mattis matrix, diagonal matrixes are easy to
exponentiate.
Peter
Vesa-Matti Sarenius skrev:
> > There is an implcit formula for calculating the n'th fibonacci number.
> > if you mail pewei at algonet.se I think I have it somewhere.
>
> with Mathematica MatrixPower, you can get large Fibonacci numbers fast.
>
> fibona[n_]:=MatrixPower[{{1,1},{1,0}},n][[1,1]]
>
> In: Timing[fibona[100000]]
>
> Out: {2.38 Second,42026927029951543...}
>
> On Pentium 120...
>
> Roman Maeders book The Mathematrica Programmer discusses more about
> making this algorithm more effective.
>
> --
> Vesa-Matti Sarenius * - Am I a man or what? - A What!*
> mailto:sarenius at paju.oulu.fi * - What? - Yes, that's right! *
> Koskitie 47 A6 FIN-90500 OULU * * * * *
> http://www.student.oulu.fi/~sarenius * * * * * * * * * * hmmmm! *
> Finland, Europe. Tel. +358-8-342236 fax.+358-8-5305045. * * * * * *
--
Peter Weijnitz