Eigenvalue localization and Neville elimination

Neville elimination is an elimination procedure alternative to Gaussian elimination and very adequate when dealing with some special classes of matrices. In this paper, we present pivoting strategies such that the radii of the Geršgorin circles of the Schur complements through Neville elimination with these pivoting strategies reduce their length and we consider classes of matrices important in many applications. We include illustrative examples comparing the results with those obtained with Gaussian elimination and showing that our hypotheses are necessary.