Analyzing Chebyshev polynomial-based geometric circulant matrices
This paper explores geometric circulant matrices whose entries are Chebyshev polynomials of the first or second kind. Motivated by our previous research on $ r- $circulant matrices and Chebyshev polynomials, we focus on calculating the Frobenius norm and deriving estimates for the spectral norm boun...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024254 |
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| author | Zoran Pucanović Marko Pešović |
| author_facet | Zoran Pucanović Marko Pešović |
| author_sort | Zoran Pucanović |
| collection | DOAJ |
| description | This paper explores geometric circulant matrices whose entries are Chebyshev polynomials of the first or second kind. Motivated by our previous research on $ r- $circulant matrices and Chebyshev polynomials, we focus on calculating the Frobenius norm and deriving estimates for the spectral norm bounds of these matrices. Our analysis reveals that this approach yields notably improved results compared to previous methods. To validate the practical significance of our research, we apply it to existing studies on geometric circulant matrices involving the generalized $ k- $Horadam numbers. The obtained results confirm the effectiveness and utility of our proposed approach. |
| format | Article |
| id | doaj-art-80073c1f68b64ed4b18def25f03fa885 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-80073c1f68b64ed4b18def25f03fa8852025-01-23T07:52:42ZengAIMS PressElectronic Research Archive2688-15942024-09-013295478549510.3934/era.2024254Analyzing Chebyshev polynomial-based geometric circulant matricesZoran Pucanović0Marko Pešović1Faculty of Civil Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, SerbiaFaculty of Civil Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, SerbiaThis paper explores geometric circulant matrices whose entries are Chebyshev polynomials of the first or second kind. Motivated by our previous research on $ r- $circulant matrices and Chebyshev polynomials, we focus on calculating the Frobenius norm and deriving estimates for the spectral norm bounds of these matrices. Our analysis reveals that this approach yields notably improved results compared to previous methods. To validate the practical significance of our research, we apply it to existing studies on geometric circulant matrices involving the generalized $ k- $Horadam numbers. The obtained results confirm the effectiveness and utility of our proposed approach.https://www.aimspress.com/article/doi/10.3934/era.2024254geometric circulant matrixmatrix normschebyshev polynomialshoradam numbers |
| spellingShingle | Zoran Pucanović Marko Pešović Analyzing Chebyshev polynomial-based geometric circulant matrices Electronic Research Archive geometric circulant matrix matrix norms chebyshev polynomials horadam numbers |
| title | Analyzing Chebyshev polynomial-based geometric circulant matrices |
| title_full | Analyzing Chebyshev polynomial-based geometric circulant matrices |
| title_fullStr | Analyzing Chebyshev polynomial-based geometric circulant matrices |
| title_full_unstemmed | Analyzing Chebyshev polynomial-based geometric circulant matrices |
| title_short | Analyzing Chebyshev polynomial-based geometric circulant matrices |
| title_sort | analyzing chebyshev polynomial based geometric circulant matrices |
| topic | geometric circulant matrix matrix norms chebyshev polynomials horadam numbers |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024254 |
| work_keys_str_mv | AT zoranpucanovic analyzingchebyshevpolynomialbasedgeometriccirculantmatrices AT markopesovic analyzingchebyshevpolynomialbasedgeometriccirculantmatrices |