Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-31T01:29:54.194Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounds for the separations of real zeros of polynomials

Part of: Polynomials, rational functions

Published online by Cambridge University Press:  09 April 2009

Peter Walker
Peter Walker
Affiliation:
College of Science, P.O. 36Sultan Qaboos UniversityAl-Khod, 123 Muscat, Sultanate of, Oman
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We measure the separation of the zeros of the polynomial f(x) = by δ(f) = mini(ai+1 − ai). We establish a bound for the amount by which the ratio δ(f′ − kf)/δ(f) exceeds 1.

MSC classification

Secondary: 26C10: Polynomials

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 330 - 342
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Henrici, P., Applied and computational complex analysis, 1 (Wiley, New York, 1974).Google Scholar
[2]Marden, M., Geomentry of polynomials (Amer. Math. Soc., Providence, 1965).Google Scholar
[3]Szegö, G. and Pólya, G., Problems and theorems in analysis, II (Springer, New York, 1976).Google Scholar
[4]Walker, P. L., ‘Separation of the zeros of polynomials’, Amer. Math. Monthly, 100 (1993), 272–273.Google Scholar
[5]Walker, P. L., ‘Upper bounds for separation of real zeros of polynomials’, Proc. Edinburgh Math. Soc., to appear.Google Scholar