부산대학교 도서관

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 $f$.
Comment: 4 pages. A software implementation can be found in algorithm vtkPolynomialSolversUnivariate , within the VTK (Visualization Toolkit) software package