Why does a'*b yield a (slightly) different result than dot(a,b)?
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I was working an building a matrix entry-wise and checking two different methods against each other and eventually found that dot(a,b) is giving me a different answer than a'*b, where a and b are both real 9948x1 column vectors. I can see that the implementation of dot uses conj(a)*b, but my vectors are real. In one example, dot(a,b) = -1.0351e-11 and a'*b = -8.6402e-12.
I think it's likely a floating point precision issue, but I'm curious about the implementation of the "*" operator and what might be leading to it. Can anyone shed some light on this?
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Walter Roberson
2017-11-28
For sufficiently large arrays, a'*b is going to invoke the high performance libraries, which are going to calculate the multiplications in multiple threads, doing partial summations, before eventually doing a final summation. Because the summations could be done in a different order than sum(conj(a).*b), the round-off can be different.
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