An implicit algorithm for computing the minimal Geršgorin set

Abstract

In this paper we present a new algorithm for the computing the minimal Geršgorin set that can be considered as an extension of the results from An algorithm for computing minimal Gerršgorin sets.

While the general approach to calculation of the boundary of the minimal Geršgorin set is kept, the core numerical calculation is changed. Namely, problem is formulated in such a way that the eigenvalue computations are replaced by LU decompositions, allowing the algorithm to be used for larger matrices more efficiently. To illustrate the benefits, we compere both algorithms on several test matrices.