On multiple roots in Descartes' rule and their distance to roots of higher derivatives

DOI10.1016/j.cam.2005.12.016zbMath1117.26014OpenAlexW2031078749MaRDI QIDQ859884

Arno Eigenwillig

Publication date: 22 January 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.12.016

zbMATH Keywords

root separationBernstein basisroot isolationDescartes-Jacobi RuleDescartes' Rule of signs

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Numerical computation of solutions to single equations (65H05) Real polynomials: location of zeros (26C10)

Related Items (4)

A generalization of Descartes rule of signs and fundamental theorem of algebra ⋮ On the complexity of the Descartes method when using approximate arithmetic ⋮ A general approach to isolating roots of a bitstream polynomial ⋮ Root refinement for real polynomials using quadratic interval refinement

Uses Software

• ISOLATE

Cites Work

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• Remarks on de la Vallée Poussin means and convex conformal maps of the circle
• Bounds on a polynomial
• Efficient isolation of polynomial's real roots.
• Bézier and B-spline techniques
• New bounds for the Descartes method
• Note on Vincent's theorem
• A refinement of the Gauss-Lucas theorem
• Algorithms in real algebraic geometry

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