1 research outputs found
Fast Computation of Sep via Interpolation-based Globality Certificates
Given two square matrices and , we propose a new approach for
computing the smallest value such that and
share an eigenvalue, where . In 2006, Gu and Overton
proposed the first algorithm for computing this quantity, called
("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, and until now, no other algorithms have been
known. Our new algorithm can be orders of magnitude faster and can solve
problems where and are of moderate size. Moreover, our method consists
of many "embarrassingly parallel" computations, and so it can be further
accelerated on multi-core hardware. Finally, we also propose the first
algorithm to compute an earlier version of sep-lambda where .Comment: Revision #3, March 22, 202