0
$\begingroup$

Is machine epsilon the largest relative error in representing a number as a floating point number?

There are so many definitions of machine epsilon. I'm starting to get confused. Isn't the machine epsilon the smallest?

$\endgroup$
  • 2
    $\begingroup$ There are nonequivalent definitions of what people call machine epsilon. What can we do? You need to ask whoever you are talking with or try to deduce from the context. $\endgroup$ – plop Sep 10 at 15:45
0
$\begingroup$

If you read "machine epsilon" you really need to look up the definition that your book uses for it. It is all over the place.

"The largest relative error" is very unlikely to be the "machine epsilon": All computers including tablets and phones in my possession have floating point arithmetic following the IEEE 754 Standard, and there the largest possible relative error is -1 or +1: Let d be the value of the least significant bit of a denormalised numbers, then a result of d/2 would be rounded to 0 for a relative error of -1; a result just a tiny bit larger than d/2 would be rounded to d, for a relative error close to 1.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.