Why does a'*b yield a (slightly) different result than dot(a,b)?

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?

[Guillaume]

Can you supply some example inputs that show the issue.

In my version (r2017b), dot is implemented as sum(conj(a).*b). With the few trial I have done, both dot(a, b) and a'*b produce the same result (but I haven't tried to create arguments whose dot product was nearly zero).

[EQ]

I'm attaching two vectors a and b that show the issue. I'm using R2015b.

[Guillaume]

Indeed with your inputs I get the same discrepancy in R2017b. No idea why.

Answer 1

[Walter Roberson]

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.