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

Document detail

ID

oai:arXiv.org:2407.00792

Topic

Mathematics - Numerical Analysis 15B05, 15A18, 47B35, 65M12, 65L06

Author

Barakitis, Nikos Loi, Valerio Serra-Capizzano, Stefano

Year

2024

listing date

8/14/2024

Keywords

glt matrix-sequences

Metrics

Abstract

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.

;Comment: Corrected locations of images and references

Barakitis, Nikos,Loi, Valerio,Serra-Capizzano, Stefano, 2024, 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