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Machine epsilon
Posted:
Feb 6, 2013 10:49 PM


My understanding of the "machine epsilon" number (eps in Matlab) is that it's the smallest floating point number such that (1+eps) > 1.
Indeed, in Matlab you get a result of true (1) with the command
>> 1 + eps > 1
Why then is it the case that
>> 1 + .7*eps > 1
also returns true? Doesn't it mean, technically speaking, that .7*eps is an even smaller machine epsilon?
I realize that the factor 0.5 is a threshold, in the sense that
>> 1 + .500000001*eps > 1 (true) >> 1 + .5*eps > 1 (false)
So, this computation involving eps has something to do with rounding. Can somebody clarify why .5000000000001*eps (for example) isn't considered machine epsilon, but eps is?
Much thanks, Jim



