Re: complex polynomials

["J.J.Green" <j dot j dot green at sheffield dot ac dot uk>]

Hi all

> I'm not familiar with this area... could you give some examples where
> it is used in practical applications (e.g. digital filters?).  Thanks.

The maximum modulus of a polynomial is the spectral
radius of the polynomial considered as an element
of the convolution algebra \ell^1, and a number of 
interesting theorems follow from this observation.
In particular, von Neumann showed that 

  ||p(T)|| <= maxmod(P)

(where ||.|| is the operator norm) for any contraction 
T on a Hilbert space. This gives a upper bound on 
the norm of a matrix p(T) if ||T|| and maxmod(p) can
be calculated. The algorithm calculates maxmod(p) for
polynomials of order ~ 200 in a second or so.

That was my motivation -- I'm not sure if anyone has used 
this estimate in practice

-j
-- 
J. J. Green, Department of Applied Mathematics, Hicks Bd.,
Hounsfield Rd.,  University of Sheffield,  Sheffield, UK. 
+44 (0114) 222 3742,  http://www.vindaloo.uklinux.net/jjg