Computationally efficient applications of the Euclidean algorithm to zero location Original Research Article

We characterize the inertia of the n × n Hankel matrix associated with a pair of real polynomials in terms of the quotients generated by the Euclidean algorithm applied to these polynomials. In this way, we solve certain classical zero-location problems at the computational cost of O(n2) arithmetic operations, which can be reduced to O(n log2 n) if fast polynomial arithmetic is used.