Take the leading terms: x^11 + 1000*x^10. Set that equal to zero. The roots are 0 and -1000. The 1.1e-16 is clearly rounding error. -999 looks like a good approximation to a root. Take the leading terms x^11 + 1000*x^10 + 500*x^9. This is x^9*(x^2 + 1000x + 500).. We get quadratic roots -999.499749749687 -and 0.5002502503129382 Root [11] is looking better and better. For x close to -1000, the "1" in the polynomial is 1e-33 of x^11, so this is ill-conditioned.
On Fri, 3 Oct 2025 at 04:56, tgs77m--- via R-help <[email protected]> wrote: > > Colleagues, > > f <- function(x) ( x^11 + 1000*x^10 + 500 *x^9 + 1 ) ^0.01 > 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 is always greater > than 0 > > why does polyroot output [11] -999.49974975+1.110223e-16i ? > > Thanks, > > 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. ______________________________________________ [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.
