A note on matrices involving the Chebyshev polynomials
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In this talk, we establish a connection between some classical topics in applied mathematics - circulant matrices and the Chebyshev polynomials. First, we define circulant matrices whose entries are the Chebyshev polynomials of the first or second kind and examine their basic properties. Then we determine the bounds of the norms of such matrices. It turns out that the obtained results can be seen as the unification and generalization of many previously obtained results on circulant matrices involving the generalized Horadam numbers. We point out one direction of applications, but it is clear that there are many possibilities. With appropriate modifications, these results can be applied in different areas, such as - statistics, data approximation, interpolation, engineering, economics, signal and image processing, numerical analysis, physics and error correcting code theory, to name but a few.
Keywords:
Chebyshev polynomials / matrix norms / circulant matrixSource:
2rd International Conference on Stochastic Dynamics and Statistical Application, 2023Funding / projects:
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200092 (University of Belgrade, Faculty of Civil Engineering) (RS-MESTD-inst-2020-200092)
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GraFarTY - CONF AU - Pucanović, Zoran PY - 2023 UR - https://grafar.grf.bg.ac.rs/handle/123456789/3115 AB - In this talk, we establish a connection between some classical topics in applied mathematics - circulant matrices and the Chebyshev polynomials. First, we define circulant matrices whose entries are the Chebyshev polynomials of the first or second kind and examine their basic properties. Then we determine the bounds of the norms of such matrices. It turns out that the obtained results can be seen as the unification and generalization of many previously obtained results on circulant matrices involving the generalized Horadam numbers. We point out one direction of applications, but it is clear that there are many possibilities. With appropriate modifications, these results can be applied in different areas, such as - statistics, data approximation, interpolation, engineering, economics, signal and image processing, numerical analysis, physics and error correcting code theory, to name but a few. C3 - 2rd International Conference on Stochastic Dynamics and Statistical Application T1 - A note on matrices involving the Chebyshev polynomials UR - https://hdl.handle.net/21.15107/rcub_grafar_3115 ER -
@conference{ author = "Pucanović, Zoran", year = "2023", abstract = "In this talk, we establish a connection between some classical topics in applied mathematics - circulant matrices and the Chebyshev polynomials. First, we define circulant matrices whose entries are the Chebyshev polynomials of the first or second kind and examine their basic properties. Then we determine the bounds of the norms of such matrices. It turns out that the obtained results can be seen as the unification and generalization of many previously obtained results on circulant matrices involving the generalized Horadam numbers. We point out one direction of applications, but it is clear that there are many possibilities. With appropriate modifications, these results can be applied in different areas, such as - statistics, data approximation, interpolation, engineering, economics, signal and image processing, numerical analysis, physics and error correcting code theory, to name but a few.", journal = "2rd International Conference on Stochastic Dynamics and Statistical Application", title = "A note on matrices involving the Chebyshev polynomials", url = "https://hdl.handle.net/21.15107/rcub_grafar_3115" }
Pucanović, Z.. (2023). A note on matrices involving the Chebyshev polynomials. in 2rd International Conference on Stochastic Dynamics and Statistical Application. https://hdl.handle.net/21.15107/rcub_grafar_3115
Pucanović Z. A note on matrices involving the Chebyshev polynomials. in 2rd International Conference on Stochastic Dynamics and Statistical Application. 2023;. https://hdl.handle.net/21.15107/rcub_grafar_3115 .
Pucanović, Zoran, "A note on matrices involving the Chebyshev polynomials" in 2rd International Conference on Stochastic Dynamics and Statistical Application (2023), https://hdl.handle.net/21.15107/rcub_grafar_3115 .