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Topic: Machine epsilon
Replies: 1   Last Post: Feb 7, 2013 1:55 AM

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 Jim Rockford Posts: 164 Registered: 6/30/06
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

Date Subject Author
2/6/13 Jim Rockford
2/7/13 James Tursa