Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form

V. Stukopin; S. Grudsky; I. Voronin; M. Barrera

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arXiv · 2111.07196

Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form

V. Stukopin·S. Grudsky·I. Voronin·M. Barrera

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Abstract

We find uniform asymptotic formulas for all the eigenvalues of certain 7-diagonal symmetric Toeplitz matrices of large dimension. The entries of the matrices are real and we consider the case where the real-valued generating function such that its first five derivatives at the one endpoint of interval are equal zero. This is not the simple-loop case considered earlier. We obtain nonlinear equations for the eigenvalues. It should be noted that our equations have a more complicated structure than the equations for the simple loop case.

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BibTeX RIS

V. Stukopin, S. Grudsky, I. Voronin, M. Barrera. 2021-11-13. Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form. https://arxiv.org/abs/2111.07196

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