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arXiv · 2208.07904

Sturm's Theorem with Endpoints

Philippe Pébay·J. Maurice Rojas·David C. Thompson
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Abstract

Sturm's Theorem is a fundamental 19th century result relating the number of real roots of a polynomial $f$ 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 $f$.

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Philippe Pébay, J. Maurice Rojas, David C. Thompson. 2022-08-16. Sturm's Theorem with Endpoints. https://arxiv.org/abs/2208.07904

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