Root finder for large problems about polynomials.jl

[Keno]

What's the license of the Fortran code and does it make any sense to translate it to Julia?

[andreasnoack]

They haven't stated the license, but I can try to ask them if MIT is okay.

I have considered writing a Julia version, but I think it would take more time than I can allow to spend.

By the way, I should add that the advantage of their method is that the companion matrix can be stored very compactly and hence it is possible to calculate the roots of polynomials of very high degree.

[hrobotron]

Any private progress on this topic? Would be interesting to compare the KU Leuven algorithm to a8c9302;
and if there were no performance penalty, I'd opt for the faster algorithm. If you have the Fortran code running, please test against a8c9302 and if the outcome will be positive, let's consider porting to native Julia.

Also, do you have any author feedback on licensing?

[andreasnoack]

Just checked my email and Watkins replied that he is fine with MIT license for the AMVW code. There is no doubt that AMVW code can handle much larger problems and I think it is faster for all problem sizes. It would be great to use the AMVW functionality for finding roots in this package. It would either require that we find a way to supply binaries of the Fortran code or port the code to Julia. Right now, I don't have much time to do any of these but if you are interested in trying it out, I can try to help.

[hrobotron]

I'd definitely opt for porting to native Julia. I will await whether my other pull requests will find their way to the pkg, then I may consider investing some work into trying and porting the AMVW code. BTW, if you have the code running (outside of Julia), can you just run few tests, what will be errors of Fortran AMVW compared to a8c9302 roots? I mean

r=something (randn, real, complex,...)
r1=roots(poly(r))
r=sort(r, lt=(a,b)->(real(a)<real(b)||imag(a)<imag(b)))
r1=sort(r1, lt=(a,b)->(real(a)<real(b)||imag(a)<imag(b)))
e=r1-r
maximum(abs(e))

or std(e).

It would be great to assure the AMVW will not give worse results, prior to replace the very standard way using full O(n^2) companion matrix. No doubt it will be faster, though.

[jverzani]

Your other pull request will find its way in soon. I was going to ask you to add a test, but see you've already got there. This would be a good addition in my opinion, though it might be best in an independent package at the outset.

[jverzani]

This was done in https://github.com/jverzani/AMRVW.jl