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MathGroup Archive 2000

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Re: Speeding up Inverting matrices.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23040] Re: Speeding up Inverting matrices.
  • From: Eckhard Hennig <hennig at itwm.uni-kl.de>
  • Date: Thu, 13 Apr 2000 02:43:26 -0400 (EDT)
  • Organization: ITWM
  • References: <8d0q3v$4oi@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

David McGloin schrieb in Nachricht <8d0q3v$4oi at smc.vnet.net>...
>I wish to solve the matrix equation Ax = b for x where A is a 24 x 24
>matrix and x and b are column matrices. Most of the values in the matrix
>are numbers (and many are equal to zero), but one remains unevaluated
>i.e element [1,10] may be 160 + d, where d is unevaluated. Currently
>we're using the command:
>
>x = {Inverse [A]. b}
>
>this works fine for the smaller matrices we use (8 x 8 and 16 x 16) but
>the calculation has now be runing for over 2 days (the smaller matrices
>may take many minutes if not seconds). The program is running on a PII
>350MHz with 64Mb of RAM. Does anyone have any ideas about how to
>optimise our calculation?


Yes, do not calculate a symbolic matrix inverse explicitly unless you really
need it. Use LinearSolve instead:

x = LinearSolve[A, b]

However, for sparse equations, I recommend to convert the matrix equation Ax
= b to a list of equations (see below) and use Solve to calculate the
solution (Solve is faster than LinearSolve for sparse symbolic equations).

x = {x1, x2, x3, ..., x24}
eqs = Thread[A.x == b]
Solve[eqs, x]

HTH,

  Eckhard

-----------------------------------------------------------
Dipl.-Ing. Eckhard Hennig      mailto:hennig at itwm.uni-kl.de
Institut fuer Techno- und Wirtschaftsmathematik e.V. (ITWM)
Erwin-Schroedinger-Strasse,  67663 Kaiserslautern,  Germany
  Voice: +49-(0)631-205-3126    Fax: +49-(0)631-205-4139
    http://www.itwm.uni-kl.de/as/employees/hennig.html

     ITWM - Makers of Analog Insydes for Mathematica
        http://www.itwm.uni-kl.de/as/products/ai
-----------------------------------------------------------





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