Sturm's Theorem with Endpoints
Symbolic Computation
2022-08-18 v1 Commutative Algebra
Abstract
Sturm's Theorem is a fundamental 19th century result relating the number of real roots of a polynomial in an interval to the number of sign alternations in a sequence of polynomial division-like calculations. We provide a short direct proof of Sturm's Theorem, including the numerically vexing case (ignored in many published accounts) where an interval endpoint is a root of .
Cite
@article{arxiv.2208.07904,
title = {Sturm's Theorem with Endpoints},
author = {Philippe Pébay and J. Maurice Rojas and David C. Thompson},
journal= {arXiv preprint arXiv:2208.07904},
year = {2022}
}
Comments
4 pages. A software implementation can be found in algorithm vtkPolynomialSolversUnivariate , within the VTK (Visualization Toolkit) software package