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Summing a list of real numbers

  • To: mathgroup at
  • Subject: [mg33416] Summing a list of real numbers
  • From: "Coleman, Mark" <mark.coleman at>
  • Date: Wed, 20 Mar 2002 01:53:42 -0500 (EST)
  • Sender: owner-wri-mathgroup at


In the course of working on an optimization problem that involves summing large lists of real numbers, a colleague of mine came across an interesting result. We compared the computational speed of different methods for summing lists:

   (1) Apply[Plus, mylist]
    (2) Dot[mylist,ListofOnes], where ListofOnes is a list of of size N of 1.0's

    (3) Tr[mylist], where Tr is the built-in matrix trace operator.

Based on our tests (where list sizes range from 100,000 to 1,000,000 elements), Method (3) is far and away the fastest. On average (3) is 5x faster than Method (2), and over 70x faster than Method (1). 

I was curious if anyone could offer an explanation.



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