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)
• 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