Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Zeration = inconsistant ?
#20
Example :

Solve

exp^[2]( 2 ln^[2](x) ) = 7

This is equivalent to

x^ln(x) = 7.

Take some real a,b >= exp(1).

a_0 = a^{ 1 / ln(b) }
b_0 = 7^{ ln(b) / ln(a) }

replacement rules :
---
a ' = a * 7^{ ln(b) }

b ' = a * b
---

a_1 = a ' ^{ 1/ln(b ') }
b_1 = 7^{ ln(b ') / ln(a ') }

repeat forever

lim n-> oo

a_n/b_n = x.

this gives x = exp( sqrt( ln(7) ) ) as it should.

Numerically we get x = 4.0348084730118923250275859453110072467762717139110...

Notice 1/x is also a solution.
If we take 0 < a,b < 1/exp(1) ( =exp(-1) ) we probably achieve that.

This numerical algorithm can probably be improved with adding some + operators at the right places ...

Still investigating.

Notice I did not use a derivative anywhere like most numerical methods do.

Also the method can probably be extended nicely to all interpretations of hyperoperators.

Extending towards complex numbers however seems difficult.
(unless we split up by variables for real and imag part )

Can zeration inprove this algoritm ?

regards

tommy1729

" So he can probably do math better than most cows , so what ? "
Ullrich mocking me on sci.math.

" Truth is that what does not go away when you stop believing in it "
tommy1729
Reply


Messages In This Thread
Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM
RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM
RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM
RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM
RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM
RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM
RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM
RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM
RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM
RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM
RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM
RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Zeration GFR 80 109,215 10/31/2016, 02:57 PM
Last Post: Stanislav
  Zeration reconsidered using plusation. tommy1729 1 3,118 10/23/2015, 03:39 PM
Last Post: MphLee
  Is this close to zeration ? tommy1729 0 2,147 03/30/2015, 11:34 PM
Last Post: tommy1729
  [2015] 4th Zeration from base change pentation tommy1729 5 6,188 03/29/2015, 05:47 PM
Last Post: tommy1729
  [2015] New zeration and matrix log ? tommy1729 1 3,351 03/24/2015, 07:07 AM
Last Post: marraco
  [2014] Inconsistant equation ? tommy1729 0 1,875 07/27/2014, 02:38 PM
Last Post: tommy1729
  base change inconsistant ? tommy1729 2 3,289 11/26/2012, 08:13 AM
Last Post: Nasser



Users browsing this thread: 1 Guest(s)