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MathGroup Archive 1995

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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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