تقرير
Sturm's Theorem with Endpoints
العنوان: | Sturm's Theorem with Endpoints |
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المؤلفون: | Pébay, Philippe, Rojas, J. Maurice, Thompson, David C. |
سنة النشر: | 2022 |
المجموعة: | Computer Science Mathematics |
مصطلحات موضوعية: | Computer Science - Symbolic Computation, Mathematics - Commutative Algebra |
الوصف: | 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 |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2208.07904 |
رقم الأكسشن: | edsarx.2208.07904 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |