[R] uniroot

[Jeff Newmiller]

Yes. This kind of issue is covered in any decent undergraduate course in numerical methods... it is not specific to R. It is also related to FAQ 7.31.
 https://en.m.wikipedia.org/wiki/Root-finding_algorithms

https://en.m.wikipedia.org/wiki/Floating-point_arithmetic#Representable_numbers,_conversion_and_rounding

On August 27, 2021 10:30:38 AM PDT, Thomas Subia via R-help <r-help using r-project.org> wrote:
>Colleagues,
>
>I've been using uniroot to identify a root of an equation. 
>As a check, I always verify that calculated root. 
>This is where I need some help.
>
>Consider the following script
>
>fun <- function(x) {x^x -23}
>
># Clearly the root lies somewhere between 2.75 and 3.00
>
>uniroot(fun, lower = 2.75, upper = 3.00,  tol = 0.001)
>
># output
>$root
>[1] 2.923125
>
>$f.root
>[1] 0.0001136763
>
># Let's verify this root.
>
>2.923125^2.923125 - 23
>
>0.0001222225
>
>This result is different than what was calculated with uniroot
>0.0001222225		# verified check using x = 2.923125
>0.0001136763		# using $f.root
>
>Does this imply that the root output of  2.923125 may need more significant
>digits displayed?
>
>I suspect that whatever root is calculated, that root may well be dependent
>on what interval one defines where the root may occur
>and what tolerance one has input.
>I am not sure that is the case, nevertheless, it's worth asking the
>question.
>
>Some guidance would be appreciated.
>
>Thanks!
>
>Thomas Subia
>
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-- 
Sent from my phone. Please excuse my brevity.