A simplified Schur-Cohn test

A new test is given for deciding whether a prescribed real polynomial of degree
n
has all its zeros inside the unit circle. The test involves examination of the sign of various linear combinations of the polynomial coefficients, as well as examination to check positive definiteness of a symmetric matrix of dimensions
\frac{1}{2}n \times \frac{1}{2}n
when
n
is even, and
\frac{1}{2}(n + 1) \times \frac{1}{2}(n + 1)
or
\frac{1}{2}(n - 1) \times \frac{1}{2}(n - 1)
when
n
is odd.