TOMS429
Localization of the Roots of a Polynomial
TOMS429
is a FORTRAN77 library which
implements ACM TOMS algorithm 429, for localization of the
roots of a polynomial.
While the text of many ACM TOMS algorithms is available online
through ACM:
http://www.acm.org/pubs/calgo
or NETLIB:
http://www.netlib.org/toms/index.html, most of the early
algorithms are not available. This is one of them. I typed it
in.
This version of the algorithm incorporates corrections and
improvements suggested by Driessen and Hunt.
Usage:

call polyan ( c, cm, n )

where C(1:N) contains the polynomial coefficients, omitting
the leading coefficient, which is assumed by normalization to
be 1, and starting with the coefficient of X^(N1); CM(1:N)
is a work vector and N is the degree of the polynomial.
Languages:
TOMS429 is available in
a FORTRAN77 version.
Reference:

HB Driessen, EW Hunt,
Remark on Algorithm 429,
Communications of the ACM,
September 1973, Volume 16, Number 9, page 579.

Paul Saylor, James Sebastian,
Algorithm 429: Localization of the Roots of a Polynomial,
Communications of the ACM,
Volume 15, Number 8, August 1972, pages 776777.
Source Code:
Examples and Tests:
List of Routines:

POLYAN determines localization information about
a polynomial;

RADIUS bounds the roots inside a ring;

BOUND returns an upper limit for the positive
real roots;

HRWTZR employs a modification of the RouthHurwitz
criterion to determine wheterh the polynomial has any roots
with positive real parts;
You can go up one level to
the FORTRAN77 source codes.
Last revised on 03 December 2005.