Tight Bounds on the Radius of Nonsingularity

  • David HartmanEmail author
  • Milan Hladík
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9553)


Radius of nonsingularity of a square matrix is the minimal distance to a singular matrix in the maximum norm. Computing the radius of nonsingularity is an NP-hard problem. The known estimations are not very tight; one of the best one has the relative error 6n. We propose a randomized approximation method with a constant relative error 0.7834. It is based on a semidefinite relaxation. Semidefinite relaxation gives the best known approximation algorithm for MaxCut problem, and we utilize similar principle to derive tight bounds on the radius of nonsingularity. This gives us rigorous upper and lower bounds despite randomized character of the algorithm.


Radius of nonsingularity Bounds Semidefinite programming 


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Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Institute of Computer Science Academy of SciencesPrague 8Czech Republic

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