On the intersection of the classes of doubly diagonally dominant matrices and S-strictly diagonally dominant matrices

Abstract

We denote by H0 the subclass of H-matrices consisting of all the matrices that lay simultaneously on the classes of doubly diagonally dominant (DDD) matrices (A = [aij ] ∈ Cn×n : |aii||ajj | ≥ k =i |aik| k =j |ajk|, i = j) and S-strictly diagonally dominant (S-SDD) matrices. Notice that strictly doubly diagonally dominant matrices (also called Ostrowsky matrices) are a subclass of H0. Strictly diagonally dominant matrices (SDD) are also a subclass of H0. In this paper we analyze some properties of the class H0 = DDD ∩ S-SDD.