Geršgorin‐type localizations of generalized eigenvalues | Zendy

Kostić V. | Zendy; Cvetković L. J. | Zendy; Varga R. S. | Zendy

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Geršgorin‐type localizations of generalized eigenvalues

Author(s) -

Kostić V.,

Cvetković L. J.,

Varga R. S.

Publication year - 2009

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.671

Subject(s) - mathematics , eigenvalues and eigenvectors , matrix (chemical analysis) , pure mathematics , diagonal , algebra over a field , combinatorics , discrete mathematics , geometry , materials science , physics , quantum mechanics , composite material

We introduce several localization techniques for the generalized eigenvalues of a matrix pair, obtained via the famous Geršgorin theorem and its generalizations. Specifically, we address the techniques of computing and graphing of the obtained localization sets of a matrix pair. The work that follows involves much about nonnegative matrices, strictly diagonally dominant (SDD) matrices, H ‐ and M ‐matrices. We show the utility of our results theoretically, as well as with numerical examples and graphs. Copyright © 2009 John Wiley & Sons, Ltd.

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