Sturm's Theorem with Endpoints

08/16/2022

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by   Philippe Pébay, et al.

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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.