ON APPROXIMATE BOUNDS OF ZEROS OF POLYNOMIALS WITHIN (original) (raw)

Bounds for the Zeros of Polynomials

2013

In this paper we find bounds for the zeros of a class of polynomials whose coefficients or their real and imaginary parts are restricted to certain conditions. Our results improve and generalize many known results in this direction.

Note on the location of zeros of polynomials

2011

In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.

On the Zeros of a Certain Class of Polynomials

International Journal of Mathematical Archive, 2013

I n this paper we prove some results on the location of zeros of a certain class of polynomials. These results generalize some known results in the theory of the distribution of zeros of polynomials.

On the location of the zeros of certain polynomials

Publications de l'Institut Math?matique (Belgrade)

We extend Aziz and Mohammad's result that the zeros, of a polynomial P (z) = n j=0 a j z j , ta j a j−1 > 0, j = 2, 3,. .. , n for certain t (> 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae iα | < a/(2n); a > 0, max |z|=a |P (z)| = |P (ae iα)|, for r < a < 2, r being the greatest positive root of the equation x n − 2x n−1 + 1 = 0, and finally obtained an upper bound, for moduli of all zeros of a polynomial, (better, in many cases, than those obtainable from many other known results).

On the behavior of zeros of polynomials of best and near-best approximation

Canadian Journal of Mathematics, 1991

Assume ƒ is continuous on the closed disk D 1 : |z| ≤ 1, analytic in |z| ≤ 1, but not analytic on D1 . Our concern is with the behavior of the zeros of the polynomials of best uniform approximation to ƒ on D1. It is known that, for such ƒ, every point of the circle |z| = 1 is a cluster point of the set of all zeros of Here we show that this property need not hold for every subsequence of the Specifically, there exists such an f for which the zeros of a suitable subsequence all tend to infinity. Further, for near-best polynomial approximants, we show that this behavior can occur for the whole sequence. Our examples can be modified to apply to approximation in the Lq -norm on |z|= 1 and to uniform approximation on general planar sets (including real intervals).

Bounds for the zeros of a polynomial

International Journal of Recent Scientific Research

In this paper we find a bound for all the zeros of a polynomial in terms of its coefficients similar to the bound given by Cauchy's classical theorem.

On the Zeros of Polynomials of Best Approximation

Journal of Approximation Theory, 1999

Given a function f, uniform limit of analytic polynomials on a compact, regular set E/C N , we relate analytic extension properties of f to the location of the zeros of the best polynomial approximants to f in either the uniform norm on E or in appropriate L q norms. These results give multivariable versions of one-variable results due to Blatt Saff, Ples niak and Wo jcik.