English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this work, we perform a spectral analysis of flipped multilevel Toeplitzsequences, i.e., we study the asymptotic spectral behaviour of$\{Y_{\boldsymbol{n}}T_{\boldsymbol{n}}(f)\}_{\boldsymbol{n}}$, where$T_{\boldsymbol{n}}(f)$ is a real, square multilevel Toeplitz matrix generatedby a function $f\in L^1([-\pi,\pi]^d)$ and $Y_{\boldsymbol{n}}$ is the exchangematrix, which has $1$s on the main anti-diagonal. In line with what we haveshown for unilevel flipped Toeplitz matrix sequences, the asymptotic spectrumis determined by a $2\times 2$ matrix-valued function whose eigenvalues are$\pm |f|$. Furthermore, we characterize the eigenvalue distribution of certainpreconditioned flipped multilevel Toeplitz sequences with an analysis thatcovers both multilevel Toeplitz and circulant preconditioners. Finally, all ourfindings are illustrated by several numerical experiments.

The asymptotic spectrum of flipped multilevel Toeplitz matrices and of certain preconditionings