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@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 > >______________________________________________ >R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >and provide commented, minimal, self-contained, reproducible code. -- Sent from my phone. Please excuse my brevity. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
