Dear Thomas, How can f be strictly positive if the leading term is an odd power of x? For large negative x, x^11 will dominate, and f should become quite negative. This argument is also supported by a graphical plot of f. Assuming that f can indeed be negative, my suspicion is that the 11th root is still a reasonable approximation to the actual root, but the gradient in this region is high and so f(x) evaluated numerically is too sensitive to small errors (that is why f(roots[[11]]) evaluates to a seemingly huge number).
Best, Lukas On Thu, Oct 2, 2025 at 6:14 PM tgs77m--- via R-help <[email protected]> wrote: > Colleagues, > > g <- function(x) ( x^11 + 1000*x^10 + 500 *x^9 + 1 ) > coeffs <- c(1, rep(0, 8), 500, 1000, 1) > roots <- polyroot(coeffs) > > Output > > [1] 0.25770068+3.958197e-01i > [2] -0.34615184+3.782848e-01i > [3] -0.04089779-4.838134e-01i > [4] 0.44124314-1.517731e-01i > [5] -0.04089779+4.838134e-01i > [6] -0.56201931-1.282822e-01i > [7] -0.34615184-3.782848e-01i > [8] 0.44124314+1.517731e-01i > [9] -0.56201931+1.282822e-01i > [10] 0.25770068-3.958197e-01i > [11] -999.49974975+1.110223e-16i > > [11] -999.49974975+1.110223e-16i makes no sense since f>0 for all x > > Why does polyroot do this? > > Thomas Subia > > ______________________________________________ > [email protected] mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > https://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ [email protected] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide https://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
