[Help-gsl] A few questions about finding all zeros of Hermite polynomial

[Jakub Narebski]

I want to find all zeros of Hermite polynomial up to fairly large order
(up to H_100). I use poly/gsl_poly_orth.c by Richard J. Mathar (found by
Google IIRC), which is not present in GSL 1.10, to calculate Hermite
polynomial using divided differences method.

Function gsl_poly_complex_solve requires polynomial in generic form;
would this cause problems wrt. numerical accuracy? It uses balanced-QR
reduction of the companion matrix; can I use LAPACK to find eigenvalues
instead of the method GSL uses (and would it make sense for N ~= 100)?
Is this the same algorithm as in opt/companion.tgz on netlib?

Is there a GSL method to multiply two polynomials in normal form,
or in divided differences representation? I'd like to try to implement
Graeffee's method of finding all zeros of polynomial.

Is perhaps Jenkins-Traub ethod of finding all zeros of polynomial (RPOLY)
considered for inclusion in GSL? Is poly/gsl_poly_orth.c?


Sincerely
-- 
Jakub Narebski
Warsaw, Poland