An Iterative Method for the Direct Hurwitz-Factorization of a Polynomial

If
N(p)
is an even polynomial in
p
with real coefficients, and further, if any zeros of
N(p)
on the imaginary axis occur to an even multiplicity,
N(p)
can be factored in several ways into the form
N(p) = Q(p){\cdot}Q(-p)
. The particular
Q(p)
which has zeros in the left half-plane only, (including, perhaps, the imaginary axis), is of importance in the theory of vibrating systems, and occurs frequently in theoretical methods of network synthesis, as for example, in Darlington's insertion loss method. It is now possible, owing to the work of the German mathematician, Bauer, to factor out
Q(p)
directly from
N(p)
, by a method which is well suited to use in digital computers. The first section of this article is essentially a translation of Bauer's original paper; the second summarizes the experience gained by writing a computer program based on his work.