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MathGroup Archive 2004

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problem with very slow matrix function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50911] problem with very slow matrix function
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Mon, 27 Sep 2004 00:42:25 -0400 (EDT)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com


Mathematica will do this function, but only very slowly...
Thsat limits the number of values and how big I can make my critical point.
I'd like a better , faster expression to do this kind of matrix 
switching function.
I'm also looking for a way to make the switch depend on a random
level as well (&& / And).  
I tried a version and it ignorred the second "and" implicit
and did it on only the first implicit expression.
As I want to do this on higher matrix level Bonacci/ Pisot
systems, I would appreciate any help.

(*  2by2 Markov sequence Critical Eigenvalue collapse of   golden mean*)
digits=19
M={{0,1},{1,1}}
Det[M]
A[n_]:=If[(Max[Eigenvalues[A[n-1]]])<12, M.A[n-1],A[Floor[(n-1)/2]]];
A[0]:={{0,1},{1,1}};
(* Critical Eigenvalue collapse at 12 of 2by2 matrices made with  golden 
mean  recurrence*)
b=Flatten[Table[A[n],{n,0,digits}]]
ListPlot[b,PlotJoined->True,PlotRange->All]

{0,1,1,1,1,1,1,2,1,2,2,3,2,3,3,5,3,5,5,8,5,8,8,13,1,2,2,3,2,3,3,5,3,5,5,8,5,8,
  
8,13,3,5,5,8,5,8,8,13,5,8,8,13,1,2,2,3,2,3,3,5,3,5,5,8,5,8,8,13,3,5,5,8,5,8,
  8,13,5,8,8,13}
Respectfully, Roger L. Bagula

tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
URL :  http://home.earthlink.net/~tftn
URL :  http://victorian.fortunecity.com/carmelita/435/ 


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