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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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-2297 |
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admjournalluguniveduua-article-22972025-10-27T20:24:52Z Dissemination of zeros of generalized derivative of a polynomial via matrix approach Mohammad, Ruqia Purohit, Mridula Liman, Abdul matrix, eigen vaues, polynomial, zero, polar derivative 30C10, 26D07 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. Lugansk National Taras Shevchenko University 2025-10-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297 10.12958/adm2297 Algebra and Discrete Mathematics; Vol 40, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297/pdf Copyright (c) 2025 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2025-10-27T20:24:52Z |
| collection |
OJS |
| language |
English |
| topic |
matrix eigen vaues polynomial zero polar derivative 30C10 26D07 |
| spellingShingle |
matrix eigen vaues polynomial zero polar derivative 30C10 26D07 Mohammad, Ruqia Purohit, Mridula Liman, Abdul Dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| topic_facet |
matrix eigen vaues polynomial zero polar derivative 30C10 26D07 |
| format |
Article |
| author |
Mohammad, Ruqia Purohit, Mridula Liman, Abdul |
| author_facet |
Mohammad, Ruqia Purohit, Mridula Liman, Abdul |
| author_sort |
Mohammad, Ruqia |
| title |
Dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| title_short |
Dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| title_full |
Dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| title_fullStr |
Dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| title_full_unstemmed |
Dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| title_sort |
dissemination of zeros of generalized derivative of a polynomial via matrix approach |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2297 |
| work_keys_str_mv |
AT mohammadruqia disseminationofzerosofgeneralizedderivativeofapolynomialviamatrixapproach AT purohitmridula disseminationofzerosofgeneralizedderivativeofapolynomialviamatrixapproach AT limanabdul disseminationofzerosofgeneralizedderivativeofapolynomialviamatrixapproach |
| first_indexed |
2025-12-02T15:46:03Z |
| last_indexed |
2025-12-02T15:46:03Z |
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1850423563476008960 |