Open AccessAn implicit algorithm for computing the minimal Gersgorin set
Author(s) -
Srđan Milićević,
Vladimir Kostić,
Lj. Cvetković,
Agnieszka Międlar
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1913229m
Subject(s) - mathematics , computation , extension (predicate logic) , set (abstract data type) , eigenvalues and eigenvectors , algorithm , core (optical fiber) , boundary (topology) , computer science , mathematical analysis , telecommunications , physics , quantum mechanics , programming language
In this paper we present a new algorithm for the computation of the minimal Gersgorin set that can be considered an extension of the results from [5]. While the general approach to calculation of the boundary of the minimal Gersgorin set is kept, the core numerical calculation is changed. Namely, the 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 compare both algorithms on several test matrices.