A new Gershgorin‐type result for the localisation of the spectrum of matrices. Issue 17 (15th July 2015)

• Record Type: Journal Article
• Authors: Dall'Acqua, Anna; Mugnolo, Delio; Schelling, Michael
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 17/18(2015)
• Page Start: 1981
• Page End: 1994
• Publication Date: 2015-07-15
• Subjects: Estimates of the spectrum of matrices -- operator matrices of unbounded operators -- 47A10 -- 15A42; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201400294
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : We present a Gershgorin's type result on the localisation of the spectrum of a matrix. Our method is elementary as it relies upon the method of Schur complements, but it outperforms the one based on the Cassini ovals of Ostrovski and Brauer. Furthermore, it yields estimates that hold without major differences in the cases of both scalar and operator matrices. Several refinements of known results are obtained.