Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-04T21:37:49.455Z Has data issue: false hasContentIssue false

Upper bounds for the separation of real zeros of polynomials

Published online by Cambridge University Press:  20 January 2009

Peter Walker
Affiliation:
College of Science P.O. Box 36 Sultan Qaboos University Al-Khod, 123 Muscat Sultanate of Oman e-mail address: [email protected]
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.

Let be a polynomial with distinct real zeros whose separation is defined by δ(f) = min i≠j(ai-aj ). We establish upper estimates for δ(f′-kf) in terms of n, k, and δ(f). The results give sufficient conditions for the inverse operator (Dkl)−1 to preserve the reality of the zeros of a polynomial.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Gelca, R., A short proof of a result on polynomials, Amer. Math. Monthly 100 (1993), 936937.Google Scholar
2. Walker, P. L., Separation of the zeros of polynomials, Amer. Math. Monthly 100 (1993), 272273.Google Scholar
3. Walker, P. L., Bounds for the separation of the zeros of polynomials. J. Australian Math. Soc., Ser.A 59 (1995), 330342.CrossRefGoogle Scholar