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Upper bounds for the separation of real zeros of polynomials

Published online by Cambridge University Press:  20 January 2009

Peter Walker
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]
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Abstract

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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 (D – kl)−1 to preserve the reality of the zeros of a polynomial.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 357 - 363
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Gelca, R., A short proof of a result on polynomials, Amer. Math. Monthly 100 (1993), 936–937.Google Scholar
2. Walker, P. L., Separation of the zeros of polynomials, Amer. Math. Monthly 100 (1993), 272–273.Google Scholar
3. Walker, P. L., Bounds for the separation of the zeros of polynomials. J. Australian Math. Soc., Ser.A 59 (1995), 330–342.CrossRefGoogle Scholar