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Pucanović, Zoran; Pešović, Marko

Chebyshev polynomials and \(r\)-circulant matrices. (English) Zbl 1510.11059

Appl. Math. Comput. 437, Article ID 127521, 13 p. (2023).
Summary: This paper connects two attractive topics in applied mathematics, \(r\)-circulant matrices and the Chebyshev polynomials. The \(r\)-circulant matrices whose entries are the Chebyshev polynomials of the first or second kind are considered. Then, estimates for spectral norm bounds of such matrices are presented. The relevance of the obtained results was verified by applying them to some of the previous results on \(r\)-circulant matrices involving various integer sequences. The acquired results justify the usefulness of the applied approach.

Cited in 1 Review

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
15B05 Toeplitz, Cauchy, and related matrices
11B83 Special sequences and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Chebyshev polynomials; \(r\)-circulant matrix; matrix norms; integer sequences

Software:

PyG; SplineCNN
Cite Review PDF
Full Text: DOI

References:

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