L. Cvetkovic, V. Kostik and R. S. Varga, A New Gergorin-type eigenvalue inclusion set, ETNA (Electronic Transactions on Numerical Analysis) 18(2004), 73-80. 

Abstract. We give a generalization of a less well-known result of Dashnic and Zusmanovich [2] from 1970, and show how this generalization compares with related results in this area.

The Gershgorin disk theorem is a simple and elegant result that localizes eigenvalues of a matrix in the complex plane. For special matrices, such as strictly diagonally dominant matrices, the Ger-shgorin disk theorem has an equivalent nonsingularity counterpart that ensures nonsingularity of these matrices. In this paper, the authors derive Gershgorin-type theorems and their nonsingularity counterpart by generalizing the concept of strict diagonal dominance.

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