Utilizzazione di proprietà delle matrici per lo studio dei polinomi ultrasferici

A system of orthogonal polinomials can be generated by a three-term recurrence relationship so that with each polinomial a certain tridiagonal matrix can be associated. Making use only of matrix properties that, besides being tridiagonal, are symmetric, positive definite, non negative and, in particular, oscillatory, some properties, partly well known, of the zeros of the ultraspherical polinomials are found and highly efficent method is proposed to compute such zeros.