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## Re: [Help-gsl] A few questions about finding all zeros of Hermite polyno

**From**: |
Brian Gough |

**Subject**: |
Re: [Help-gsl] A few questions about finding all zeros of Hermite polynomial |

**Date**: |
Tue, 20 Nov 2007 18:59:36 +0000 |

**User-agent**: |
Wanderlust/2.14.0 (Africa) Emacs/22.1 Mule/5.0 (SAKAKI) |

At Sun, 18 Nov 2007 14:15:26 +0100,
Jakub Narebski wrote:
>* 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? *
For orthogonal polynomials there are specialised methods for finding
the roots, e.g. as used for finding the abscissae in Gauss-Hermite
integration -- which are the roots of Hermite polynomials. These will
work much better than a general polynomial solver as they use the
recurrence relations directly to do Newton-Raphson steps.
>* Is there a GSL method to multiply two polynomials in normal form,*
>* or in divided differences representation?*
No, but I would accept some functions for this.
>* Is perhaps Jenkins-Traub ethod of finding all zeros of polynomial (RPOLY)*
>* considered for inclusion in GSL? Is poly/gsl_poly_orth.c?*
These require some more feedback and testing from users to get
incorporated.
--
Brian Gough
Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/