2013•PAMMOpen access

Diagonal scaling in eigenvalue localization for the Schur complement

Ljiljana Cvetković, Maja Nedović

Abstract

Abstract Geršgorin theorem is a well‐known result in eigenvalue localization area. In this paper, using diagonal scaling method, we obtain more Geršgorin‐type localizations for the eigenvalues of the Schur complement using the entries of the original matrix instead of the entries of the Schur complement. We deal with classes of matrices with some form of diagonal dominance. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Key concepts: Schur complement, Diagonal, Eigenvalues and eigenvectors, Scaling, Complement (music), Mathematics, Pure mathematics, Mathematical analysis