A note on eigenvalues and singular values of variable Toeplitz matrices and matrix-sequences, with application to variable two-step BDF approximations to parabolic equations
<|reference_start|>A note on eigenvalues and singular values of variable Toeplitz matrices and matrix-sequences, with application to variable two-step BDF approximations to parabolic equations: Here, we consider a more general class of matrix-sequences and we prove that they belong to the maximal $*$-algebra of generalized locally Toeplitz (GLT) matrix-sequences. Then, we identify the associated GLT symbols and GLT momentary symbols in the general setting and in the specific case, by providing in both cases a spectral and singular value analysis. More specifically, we use the GLT tools in order to study the asymptotic behaviour of the eigenvalues and singular values of the considered BDF matrix-sequences, in connection with the given non-uniform grids. Numerical examples, visualizations, and open problems end the present work.<|reference_end|>
@article{barakitis2024a,
    title={A note on eigenvalues and singular values of variable Toeplitz matrices
  and matrix-sequences, with application to variable two-step BDF
  approximations to parabolic equations},
    author={Nikos Barakitis, Valerio Loi, Stefano Serra-Capizzano},
    journal={arXiv preprint arXiv:2407.00792},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00792},
    primaryClass={math.NA cs.NA}
}