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MathGroup Archive 2000

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Re: multiplying a list of matrices together

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23535] Re: multiplying a list of matrices together
  • From: "William F. Campbell" <valentin at wam.umd.edu>
  • Date: Sat, 20 May 2000 03:10:15 -0400 (EDT)
  • Organization: UMD Dept. of Meteorology
  • References: <8fqqrr$h3k@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

> on a previous message someone asked how to multiply a list of
> matrices together. Two solutions suggested were:
> 
> MapThread[Dot, list, 0]
> Dot@@list
> 
> Both of these work, but I'd like to point out that Mathematica does
> NOT choose the best ordering for the multiplications, thereby
> unnecessarily spending too much computation time if the matrices
> aren't all of the same dimensions.
> 
> There's a standard dynamic programming algorithm to choose the order
> in which to perform the multiplications so as to minimize the total
> operation count. Any decent book on data structures and algorithms,
> such as "Introduction to Algorithms" by Cormen, Leiserson and Rivest,
> will have a description of the algorithm in question. I remember
> seeing a Mathematica implementation once, but I can't remember where.
> 
> Wagner

It's in David Wagner's book Power Programming with Mathematica: The
Kernel, page 168-174.

Bill Campbell


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