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Considering the Taylor series with remainder,

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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  • The maximum roundoff error of what quantity? – Carl Christian Oct 05 '20 at 23:04
  • @CarlChristian I do not know how to explain this briefly but I hope that attaching a screenshot of the question would help. Link: https://ibb.co/Hp5Btvj –  Oct 05 '20 at 23:23
  • 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. – Carl Christian Oct 06 '20 at 08:28
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    This, https://math.stackexchange.com/questions/2497660/central-difference, could be a similar question. Also relevant could be https://math.stackexchange.com/questions/3600018/why-do-we-need-numerical-method-of-differentiation, https://math.stackexchange.com/questions/2488262/how-to-approximate-relative-error, or https://math.stackexchange.com/questions/2019573/4th-order-accurate-difference-formula-less-accurate – Lutz Lehmann Oct 06 '20 at 18:17

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