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Asked: 2026-05-13T10:23:25+00:00

R question: Looking for the fastest way to NUMERICALLY solve a bunch of arbitrary

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R question: Looking for the fastest way to NUMERICALLY solve a bunch of arbitrary cubics known to have real coeffs and three real roots. The polyroot function in R is reported to use Jenkins-Traub’s algorithm 419 for complex polynomials, but for real polynomials the authors refer to their earlier work. What are the faster options for a real cubic, or more generally for a real polynomial?

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1 Answer

  1. Editorial Team

    Fleshing out Arietta’s answer above:

    > a <- c(1,3,-4)
> m <- matrix(c(0,0,-a[1],1,0,-a[2],0,1,-a[3]), byrow=T, nrow=3)
> roots <- eigen(m, symm=F, only.values=T)$values

    Whether this is faster or slower than using the cubic solver in the GSL package (as suggested by knguyen above) is a matter of benchmarking it on your system.

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