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

```

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