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
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914905106415616 |
|---|---|
| author | Barakitis, Nikos Loi, Valerio Serra-Capizzano, Stefano |
| author_facet | Barakitis, Nikos Loi, Valerio Serra-Capizzano, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 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 Barakitis, Nikos Loi, Valerio Serra-Capizzano, Stefano Numerical Analysis 15B05, 15A18, 47B35, 65M12, 65L06 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. |
| 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 |
| topic | Numerical Analysis 15B05, 15A18, 47B35, 65M12, 65L06 |
| url | https://arxiv.org/abs/2407.00792 |