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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

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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