Relationship Between Geršgorin‐type Theorems for Certain Subclasses of H‐Matrices

It is well known that the eigenvalue inclusion domain can be obtained by Geršgorin theorem. It is also known that the Geršgorin theorem is equivalent to the statement that each strictly diagonally dominant (SDD) matrix is nonsingular. Similarly, statements about nonsingularity of some classes of matrices, which are generalizations of SDD class, produce new Geršgorin‐type theorems for eigenvalue inclusion domain. In this paper we will consider some subclasses of H‐matrices and corresponding (Geršgorin‐type) eigenvalue inclusion theorems. Finally, we will establish relationship between given inclusion domains.