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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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2025
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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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