Using Optimization to Extract Roots of Real Coefficient Polynomials

[ttw]

Using optimization has been around for a while. It's worth examining. One idea that has been used is squaring the objective function and noting that zeros are now minima. I think that non-zero minima may correspond to pairs of complex roots but I haven't done the math. It's useful to separate roots so that local methods may work better. Graeffe's root-squaring method is often used. There are still some useful things being done.


https://arxiv.org/pdf/1501.02168.pdf
https://www.jstor.org/stable/2690148?seq...b_contents
https://people.mpi-inf.mpg.de/~msagralo/...tation.pdf
http://eprints.maths.ox.ac.uk/16/1/mekwi.pdf