How to go about computing the maximum roundoff error?

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Asked 3 years, 11 months ago

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Considering the Taylor series with remainder,

It is known that the function evaluations f(x+h) and f(x-h) in floating arithmetic are not exact.

Assuming that Floating Point evaluations are the respective floating point evaluations of f(x+h) and f(x-h), where ϵ< ϵ_MACH.

How to go about computing the maximum roundoff error?

I have tried working this out and I have been coming to the conclusion that the maximum error is ϵ_MACH. However, I doubt that this is correct.

Would anyone mind showing me how to work this out?

Arctic Char

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asked Oct 5, 2020 at 22:44

user815267

$\begingroup$ The maximum roundoff error of what quantity? $\endgroup$
– Carl Christian
Commented Oct 5, 2020 at 23:04
$\begingroup$ @CarlChristian I do not know how to explain this briefly but I hope that attaching a screenshot of the question would help. Link: ibb.co/Hp5Btvj $\endgroup$
– user815267
Commented Oct 5, 2020 at 23:23
$\begingroup$ We all have to write questions and answers which are searchable. Images are not searchable and third party images vanish all the time. Take the time you need to write out your question clearly as well as your current approach. $\endgroup$
– Carl Christian
Commented Oct 6, 2020 at 8:28
1

$\begingroup$ This, math.stackexchange.com/questions/2497660/central-difference, could be a similar question. Also relevant could be math.stackexchange.com/questions/3600018/…, math.stackexchange.com/questions/2488262/…, or math.stackexchange.com/questions/2019573/… $\endgroup$
– Lutz Lehmann
Commented Oct 6, 2020 at 18:17

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