Minimal sets alternative to minimal Geršgorin sets
Localization regions for the real eigenvalues or the real parts of the eigenvalues of a given real matrix \(A\) were studied by \textit{J. M. Penã} [SIAM J. Matrix Anal. Appl. 22, No.~4, 1027--1037 (2001; Zbl 0986.15015)], who introduced the notions of row \(\mathcal B\)-set and \(\mathcal B\)-set. In the present paper the notions of minimal row \(\mathcal B\)-set and minimal \(\mathcal B\)-set are introduced. Comparison is made between the notions with the minimal Geršgorin set. Some properties of the minimal \(\mathcal B\)-set are obtained via a new function.
scientific article; zbMATH DE number 5711849
scientific article