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

Given two square matrices $A$ and $B$, we propose a new approach forcomputing the smallest value $\varepsilon \geq 0$ such that $A+E$ and $A+F$share an eigenvalue, where $\|E\|=\|F\|=\varepsilon$. In 2006, Gu and Overtonproposed the first algorithm for computing this quantity, called$\mathrm{sep}_\lambda(A,B)$ ("sep-lambda"), using ideas inspired from anearlier algorithm of Gu for computing the distance to uncontrollability.However, the algorithm of Gu and Overton is extremely expensive, which limitsit to the tiniest of problems, and until now, no other algorithms have beenknown. Our new algorithm can be orders of magnitude faster and can solveproblems where $A$ and $B$ are of moderate size. Moreover, our method consistsof many "embarrassingly parallel" computations, and so it can be furtheraccelerated on multi-core hardware. Finally, we also propose the firstalgorithm to compute an earlier version of sep-lambda where $\|E\| +\|F\|=\varepsilon$.

Fast Computation of Sep$_\lambda$ via Interpolation-based Globality Certificates