Volume 3, Issue 3
On the Rate of Overconvergence of the Generalized Enestrom-Kakeya Functional for Polynomials
DOI:

J. Comp. Math., 3 (1985), pp. 275-288

Published online: 1985-03

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• Abstract

The classical Enstrom-Kakeya Theorem, which provides an upper dound for the moduli of zeros of any polynomial with positive coefficients, has been recently extended by Anderson, Saff and Verga to the case of any complex polynomial having no zeros on the ray [0,$\infinite$) Their extension is sharp in the sense that, given such a complex polynomials $p_n(z)$ of degree n›=1, a sequence of multiplier polynomial can be found for which the Enestrom-Kakeya upper bound, applied to the produces QXP, convergences, in the limit as i tends to $\infinite$, to the maximum of the moduli of the zeros of p. Here, the rate of convergence of these upper boundsis studied. It is shown that the obatined rate of convergence is best possible.

• Keywords

@Article{JCM-3-275, author = {Richard S. Varga and Wen-Da Wu}, title = {On the Rate of Overconvergence of the Generalized Enestrom-Kakeya Functional for Polynomials}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {3}, pages = {275--288}, abstract = { The classical Enstrom-Kakeya Theorem, which provides an upper dound for the moduli of zeros of any polynomial with positive coefficients, has been recently extended by Anderson, Saff and Verga to the case of any complex polynomial having no zeros on the ray [0,$\infinite$) Their extension is sharp in the sense that, given such a complex polynomials $p_n(z)$ of degree n›=1, a sequence of multiplier polynomial can be found for which the Enestrom-Kakeya upper bound, applied to the produces QXP, convergences, in the limit as i tends to $\infinite$, to the maximum of the moduli of the zeros of p. Here, the rate of convergence of these upper boundsis studied. It is shown that the obatined rate of convergence is best possible. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9624.html} }
TY - JOUR T1 - On the Rate of Overconvergence of the Generalized Enestrom-Kakeya Functional for Polynomials AU - Richard S. Varga & Wen-Da Wu JO - Journal of Computational Mathematics VL - 3 SP - 275 EP - 288 PY - 1985 DA - 1985/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9624.html KW - AB - The classical Enstrom-Kakeya Theorem, which provides an upper dound for the moduli of zeros of any polynomial with positive coefficients, has been recently extended by Anderson, Saff and Verga to the case of any complex polynomial having no zeros on the ray [0,$\infinite$) Their extension is sharp in the sense that, given such a complex polynomials $p_n(z)$ of degree n›=1, a sequence of multiplier polynomial can be found for which the Enestrom-Kakeya upper bound, applied to the produces QXP, convergences, in the limit as i tends to $\infinite$, to the maximum of the moduli of the zeros of p. Here, the rate of convergence of these upper boundsis studied. It is shown that the obatined rate of convergence is best possible.