The Schur-Cohn algorithm revisited (Q1269745)

The following question was open since 1921: how to solve the singularities of the algorithm of Schur-Cohn. The aim of the Schur-Cohn algorithm is to compute the number of roots of a complex polynomial in the open unit disc. This problem is solved. The author provides an algorithm with complexity in \(O(d^2)\) arithmetic operations which computes in any case the number of roots of a complex polynomial in the open unit disc. It can be used to study polynomials which depend on parameters. It is well adapted to computer algebra. In the following the author shows how to use bezoutians and hermitian forms to compute the number of roots in the unit disc.