large linear systems

• Subject: [mg2564] large linear systems
• From: renzoni at fexphds04.tu-graz.ac.at (FERRUCCIO Renzoni)
• Date: Tue, 21 Nov 1995 09:24:06 -0500
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.

```Dear wizs,
I have some doubts about solving large linear systems.
Suppose that I have to solve:

m.x = v

with m being a symbolic and complicated matrix and v a vector.
The critical point is to find a way to get an answer short enough to be
processed by some combination of Simplify, Together, Expand ...
I tried:
1) LinearSolve[m,v]
2) ics = {x1,x2,x3,x4,x5,x6,x7,x8,x9};

com[i_] := Apply[ PolynomialGCD, m[[i]] ]

Do[ eqn[i] = {Factor @ Numerator @ Together @
((m[[i]].ics-v[[i]])/com[i])
== 0},{i,1,9}]

eq = Join[ Flatten[ Table[eqn[i],{i,1,9}]]];

sol = ics /. Solve[eq,ics][[1]];

The strange thing is that the (2) produce an answer shorter than (1).
That's strange because I supposed that a routine (LinearSolve) produced
especially for a linear system worked more efficiently that a generic
routine for any kind of equations (or systems of equations).
My question is: does anyone knows some better way to solve a symbolic
linear system without producng enourmous expressions which cannot be
processed by Mathematica?

Thanks a lot

F. Renzoni

```

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