It is well known that the spectrum of a given matrix A belongs to the GerÅ¡gorin set (A), as well as to the GerÅ¡gorin set applied to the transpose of A, (AT). So, the spectrum belongs to theirâ€¦ (More)

The aim of the presentation is to introduce some new localization techniques for generalized eigenvalues of a matrix pair obtained via famous GerÅ¡gorin theorem and its different generalizations.â€¦ (More)

It is well-known [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246â€“251, [1]] that the Schur complement of a strictly diagonally dominantâ€¦ (More)

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

The eigenvalue localization problem is very closely related to the $H$ -matrix theory. The most elegant example of this relation is the equivalence between the GerÅ¡gorin theorem and the theorem aboutâ€¦ (More)

In this paper, we consider the localization of generalized eigenvalues, and we discuss ways in which the Gersgorin set for generalized eigenvalues can be approximated. Earlier, Stewart proposed anâ€¦ (More)

In the recent paper of Bai and Su a class of parallel decomposition-type accelerated overrelaxation (PDAOR) methods suitable to the SIMD-systems is established and convergence conditions areâ€¦ (More)