[Jprogramming] operations on polynomials

[Boyko Bantchev]

On 9/11/06, Eugene McDonnell <eemcd at mac.com> wrote:
> Boyko,
>
> Does my article in Vector 14.1 (July 1997) have any relevance to your
> technique? It uses determinants on matrices with boxed elements.

Eugene,

If you mean whether the Horner's rule applies to computing
determinants on matrices of polynomial representations,
then no, I do not see connection.
But surely the method applies to computing the
characterisic polynomial of the matrix with the matrix itself
as an argument.  So instead of computing a7, a8, and +/a8
in the article, which is a powers-based computation, one
could do the multiply-and-add iteration as prescribed by
the Horner's rule.  This should reduce the total number of
arithmetic operations.  All it takes is replacing * with
multiplication on matrices.

Regards,
  Boyko