Ljiljana Cvetković

H-matrix theory vs. eigenvalue localization

The eigenvalue localization problem is very closely related to the

Infinity norm bounds for the inverse of Nekrasov matrices

H

A new subclass of H-matrices

-matrix theory. The most elegant example of this relation is the equivalence between the Geršgorin theorem and the theorem about nonsingularity of SDD (strictly diagonally dominant) matrices, which is a starting point for further beautiful results in the book of Varga [19]. Furthermore, the corresponding Geršgorin-type theorem is equivalent to the statement that each matrix from a particular subclass of

A note on the convergence of the MSMAOR method for linear complementarity problems

H

A simple generalization of Geršgorin's theorem

-matrices is nonsingular. Finally, the statement that all eigenvalues of a given matrix belong to minimal Geršgorin set (defined in [19]) is equivalent to the statement that every

Eigenvalue Localization Refinements for Matrices Related to Positivity

H

Further results on H-matrices and their Schur complements

-matrix is nonsingular. Since minimal Geršgorin set remained unattainable, a lot of different Geršgorin-type areas for eigenvalues has been developed recently. Along with them, a lot of new subclasses of

Max-norm bounds for the inverse of S-Nekrasov matrices

H

Geršgorin‐type localizations of generalized eigenvalues

-matrices were obtained. A survey of recent results in both areas, as well as their relationships, will be presented in this paper.

New subclasses of block H-matrices with applications to parallel decomposition-type relaxation methods

From the application point of view, it is important to have a good upper bound for the maximum norm of the inverse of a given matrix A. In this paper we will give two simple and practical upper bounds for the maximum norm of the inverse of a Nekrasov matrix.