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Suppose you want to perform two sums: one is a sum of 10 scalar variables, and one is a matrix sum of a pair of two-dimensional arrays, with dimensions 10 by 10. For now let’s assume only the matrix sum is parallelizable; What speed-up do you get with 10 versus 40 processors?

My Understanding:

10x10 matrix + 10 scalar variables = 110t

With 10 processors, (100/10)t + 10t = 20t

Speed-up=110/20=5.5;

With 40 processors, (100/40)t + 10t = 12.5t

Speed-up=110/12.5=8.8;

It is given in the solution book that we get about 55% of the potential speed-up with 10 processors, but only 22% with 40.

I understand the 55% but how does that 22% come?

venkywonka
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  • `5.5/10==0.55` and `8.8/40==0.22` ? Surely ? – High Performance Mark Nov 07 '17 at 19:38
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    **Nota Bene:** What is your formal definition of a term "speed-up"? Is it the very same, as Alan Karp has used in February 1986 ( then IBM Palo Alto Scientific Center, later HP ) in his Letter to the Editor, CACM Forum, offering a prize money for any +200x speedup on his defined problem classes, or some other? ( Never hunt figures to match without being safe first on the meaning of each and every term ... be it in a Lecturer's book or anywhere else ... hunting vapourised shadows in the morning Sun is way easier task ... ) – user3666197 Nov 07 '17 at 20:08

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