Analyzing Chebyshev polynomial-based geometric circulant matrices

Zoran Pucanović; Marko Pešović; Zoran Pucanović; Marko Pešović

doi:10.3934/era.2024254

Electronic Research Archive

2024, Volume 32, Issue 9: 5478-5495. doi: 10.3934/era.2024254

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Research article

Analyzing Chebyshev polynomial-based geometric circulant matrices

Zoran Pucanović ,
Marko Pešović ^,

Faculty of Civil Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, Serbia

Received: 13 July 2024 Revised: 13 September 2024 Accepted: 18 September 2024 Published: 26 September 2024

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.
- geometric circulant matrix,
- matrix norms,
- Chebyshev polynomials,
- Horadam numbers
Citation: Zoran Pucanović, Marko Pešović. Analyzing Chebyshev polynomial-based geometric circulant matrices[J]. Electronic Research Archive, 2024, 32(9): 5478-5495. doi: 10.3934/era.2024254

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Abstract

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.

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