Bounds for zeros of Meixner and Kravchuk polynomials

The zeros of certain different sequences of orthogonal polynomials interlace in a well-defined way. The study of this phenomenon and the conditions under which it holds lead to a set of points that can be applied as bounds for the extreme zeros of the polynomials. We consider different sequences of the discrete orthogonal Meixner and Kravchuk polynomials and use mixed three-term recurrence relations, satisfied by the polynomials under consideration, to identify bounds for the extreme zeros of Meixner and Kravchuk polynomials.

On Numerical Radius of a Matrix and Estimation of Bounds for Zeros of a Polynomial

We obtain inequalities involving numerical radius of a matrixA∈Mn(ℂ). Using this result, we find upper bounds for zeros of a given polynomial. We also give a method to estimate the spectral radius of a given matrixA∈Mn(ℂ)up to the desired degree of accuracy.