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MathGroup Archive 1997

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Re: Newbie question: big matrix calculations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9322] Re: Newbie question: big matrix calculations
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 27 Oct 1997 02:47:38 -0500
  • Organization: University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

Dennis Wayne Scott wrote:
> 
> This is the first time I've ever been in this newsgroup, so please try
> to excuse anything I do/say that's silly to the experts...
> 
> I have three 100x100 sparse (diagonal) matrices (matrxD, matrxU, and
> matrxL) and three 100x1 matrices (b, x2, and x1), and I'm performing
> several operation on them:
> 
> x2 = -Inverse[matrxD].(matrxL+matrxU).x1+Inverse[matrxD].b;

You are effectively finding the fixed point:

	FixedPoint[Inverse[matrixD] . (b - (matrixL + matrixU) . #) & , x1, 
		SameTest -> (Max[Abs[#2 - #1]] < 1/10^5 & )]

	{1.19247,1.65412,1.62856,1.27819,0.711273}

This is considerably faster because you only compute Inverse[matrixD]
once (rather than twice each iteration).  Note that you get a further
speed up if your initial guess is numerical (floating point) rather
than exact.

However, for this problem, rearranging the matrix equations permits
exact solution:

	N[Inverse[matrixD + (matrixL + matrixU)] . b]

	{1.19248,1.65414,1.62857,1.2782,0.711278}

This is very fast even for 100x100 matrices!  

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at physics.uwa.edu.au  AUSTRALIA                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


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