Schur-Cohn sub-transforms of a polynomial
Let \(P\) be a polynomial of degree \(d\). The number of zeros of \(P\) lying inside \(| z|<1\) can be found (with some exceptions) by the Schur- Cohn algorithm. This constructs a sequence of polynomials \(TP, T^ 2 P,\dots\) where the degree of \(T^ k P\) is deemed to be \(d-k\) even if the coefficient of \(x^{d-k}\) is zero. (For details see, e.g., \textit{P. Henrici} [Applied and computational complex analysis. Vol. I, 493-496 (Wiley, 1988; Zbl 0635.30001)].) The coefficients in the sequence grow exponentially, but it is permissible to divide through each \(T^ i P\) by a numerical factor, and in the present paper it is shown that this can be done in such a way that the coefficients, while still integers, grow much more slowly, thus speeding up the computation.
scientific article; zbMATH DE number 627601