Dissemination of zeros of generalized derivative of a polynomial via matrix approach
A polynomial of degree \(n\) is denoted by \(p(z):=\sum\limits_{j=0}^{n} a_{j}z^{j}\). Then, by classical Cauchy's result, $$|z|\le 1+ \max\bigg(\left|\frac {a_{n-1}}{a_{n}}\right|, \left|\frac {a_{n-2}}{a_{n}}\right|, \left|\frac {a_{n-3}}{a_{n}}\right|,...,\left|\frac {a_{0}}{a_{n}}\right|\bi...
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| Дата: | 2025 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2025
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | A polynomial of degree \(n\) is denoted by \(p(z):=\sum\limits_{j=0}^{n} a_{j}z^{j}\). Then, by classical Cauchy's result, $$|z|\le 1+ \max\bigg(\left|\frac {a_{n-1}}{a_{n}}\right|, \left|\frac {a_{n-2}}{a_{n}}\right|, \left|\frac {a_{n-3}}{a_{n}}\right|,...,\left|\frac {a_{0}}{a_{n}}\right|\bigg)$$ contains all of \(p(z)\)'s zeros. In order to improve on classical Cauchy finding, we will extend such results in this study to the polar derivative of an algebraic polynomial using matrix technique. |
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