# Fast Computation of Sep_λ via Interpolation-based Globality Certificates

Given two square matrices A and B, we propose a new algorithm for computing the smallest value ε≥ 0 such that A+E and A+F share an eigenvalue, where E=F=ε. In 2006, Gu and Overton proposed the first algorithm for computing this quantity, called sep_λ(A,B) ("sep-lambda"), using ideas inspired from an earlier algorithm of Gu for computing the distance to uncontrollability. However, the algorithm of Gu and Overton is extremely expensive, which limits it to the tiniest of problems. Our new algorithm can be orders of magnitude faster and can scale up to problems where A and B are of moderate size. Furthermore, our algorithm consists of computations which are also embarrassingly parallel, and so can be further accelerated on multi-core hardware.

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