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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we are concerned with the inversion of circulant matrices andtheir quantized tensor-train (QTT) structure. In particular, we show that theinverse of a complex circulant matrix $A$, generated by the first column of theform $(a_0,\dots,a_{m-1},0,\dots,0,a_{-n},\dots, a_{-1})^\top$ admits a QTTrepresentation with the QTT ranks bounded by $(m+n)$. Under certain assumptionson the entries of $A$, we also derive an explicit QTT representation of$A^{-1}$. The latter can be used, for instance, to overcome stability issuesarising when numerically solving differential equations with periodic boundaryconditions in the QTT format.

Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices