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Solving a recursive system of 3x3 linear systems...

• To: mathgroup at smc.vnet.net
• Subject: [mg57813] Solving a recursive system of 3x3 linear systems...
• From: Kees van Schaik <schaik at math.uni-frankfurt.de>
• Date: Thu, 9 Jun 2005 05:17:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi everybody,

I'm looking at a recursive system where at each l-th step the three 
variables a[i,l] (1 <= i <= 3) have to be solved from a system of three 
linear equations  involving  the previously solved  a[i,l+1], ...., 
a[i,k]  (1 <= i <= 3) (so the iterator l runs back, starting from some 
value k). My goal is to find a closed form "direct formula" for the 
a[i,l], that is a formula that expresses each a[i,l] in terms of the 
starting values a[i,k]'s and the the other known constants involved. 
More precisely, the code for finding the first few steps of this 
recursive system looks like this:



(detail without meaning: in the above code the system starts from k+1 
instead of k). All the B[.,.]'s, beta[.,.]'s and d[.]'s are in principle 
known constants, as are the starting values a[i,k] for each 1 <= i <= 3.

Now, if I try to let Mathemetica just run through the system using the 
code above, it chokes already at the third step and the expressions of 
the second step are already pretty terrible (a lot of lines...). Is 
there any chance of using Mathematica some way to find (which is 
probably even a lot more difficult than just running through the 
system...) those direct formulas for the a[i,l]'s (so, only dependent on 
the a[i,k]'s, B[.,.]'s, beta[.,.]'s and d[.]'s)??

Any help is very much appreciated and thanks in advance,

Kees