Tight Bounds on the Radius of Nonsingularity

0459146 - ÚI 2017 RIV CH eng C - Conference Paper (international conference)
Hartman, David - Hladík, M.
Tight Bounds on the Radius of Nonsingularity.
Scientific Computing, Computer Arithmetic, and Validated Numerics. Revised Selected Papers. Cham: Springer, 2016 - (Nehmeier, M.; Wolff von Gudenberg, J.; Tucker, W.), s. 109-115. Lecture Notes in Computer Science, 9553. ISBN 978-3-319-31768-7. ISSN 0302-9743.
[SCAN 2014. International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics /16./. Würzburg (DE), 21.09.2014-26.09.2014]
R&D Projects: GA ČR GA13-17187S
Grant - others:GA ČR(CZ) GA13-10660S
Institutional support: RVO:67985807
Keywords : radius of nonsingularity * bounds * semidefinite programming
Subject RIV: IN - Informatics, Computer Science

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.
Permanent Link: http://hdl.handle.net/11104/0259385