Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?

Fayyaz Ahmad, Eman S. Alaidarous, Dina Abdullah Alrehaili, Sven-Erik Ekström, Isabella Furci, Stefano Serra Capizzano. Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?. Numerical Algorithms, 78(3):867-893, 2018. [doi]

@article{AhmadAAEFC18,
  title = {Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?},
  author = {Fayyaz Ahmad and Eman S. Alaidarous and Dina Abdullah Alrehaili and Sven-Erik Ekström and Isabella Furci and Stefano Serra Capizzano},
  year = {2018},
  doi = {10.1007/s11075-017-0404-z},
  url = {https://doi.org/10.1007/s11075-017-0404-z},
  researchr = {https://researchr.org/publication/AhmadAAEFC18},
  cites = {0},
  citedby = {0},
  journal = {Numerical Algorithms},
  volume = {78},
  number = {3},
  pages = {867-893},
}