Polynomial minimum root separation-Reference-Cited by-同舟云学术

Polynomial minimum root separation

Published:1979 Issue:145 Volume:33 Page:327-336
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Rump Siegfried M.

Abstract

The minimum root separation of an arbitrary polynomial P is defined as the minimum of the distances between distinct (real or complex) roots of P. Some asymptotically good lower bounds for the root separation of P are given, where P may have multiple zeros. There are applications in the analysis of complexity of algorithms and in the theory of algebraic and transcendental numbers.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1979-33-145/S0025-5718-1979-0514828-8/S0025-5718-1979-0514828-8.pdf

Reference20 articles.

1. A. CAUCHY, "Analyse algébrique," in Oeuvres Complètes, II série, tome III, p. 398, formula (48), Paris, 1847.

2. The minimum root separation of a polynomial;Collins, George E.;Math. Comp.,1974

3. G. E. COLLINS & R. G. K. LOOS, "Polynomial real root isolation by differentiation," Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation, August 1976, pp. 15-25.

4. Approximation of algebraic numbers by algebraic numbers;Güting, R.;Michigan Math. J.,1961

Cited by 20 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The number of solutions to the trinomial Thue equation;Functiones et Approximatio Commentarii Mathematici;2023-12-15

2. Separation bounds for polynomial systems;Journal of Symbolic Computation;2020-11

3. The Operator Approach to Entropy Games;Theory of Computing Systems;2019-05-30

4. Complex Spherical Codes with Three Inner Products;Discrete & Computational Geometry;2018-07-16

5. Improving root separation bounds;Journal of Symbolic Computation;2018-01