Scaling technique for Partition-Nekrasov matrices

On a Simple Scaling Condition for H−matrices and Applications

“…In literature, there are several subclasses of H−matrices that are introduced or further researched through a construction of special diagonal scaling matrices, see [3,7,17,18]. We apply the type of scaling from [3] in the next section in order to obtain spectra information for Schur complements.…”

“…Spectra localizations and closure properties for Schur complements of some special matrices were researched in [4,5,6,9,10,13,15,17].…”

“…The benefit of this result is that it allows us to construct a localization area for the spectrum of Schur complement matrix A/α by scaling those Geršgorin disks of the original matrix A that correspond to α. Notice that results of this type are obtained for P H−matrices, see [13], for Partition-Nekrasov matrices, see [17] and for SDD 1 matrices, see [14], only with different constructions of corresponding scaling matrices.…”

Norm bounds for the inverse and error bounds for linear complementarity problems for {P1,P2}-Nekrasov matrices

“…The diagonal matrix W is called a scaling matrix for the given matrix A. For some subclasses of H-matrices we know how to construct a corresponding scaling matrix, which can be used further in obtaining eigenvalue localization, investigation of Schur complement properties, see [8,10,11,31,33], or in determining error bounds for linear complementarity problems, see [18]. As stated in [1], for any nonsingular…”