Euclidean norm estimates of the inverse of some special block matrices

In this paper we start from the known lower bounds for minimal singular value of the matrices possessing certain kind of the diagonal dominance property, and derive Euclidean norm estimates of the inverses of several new subclasses of the block H-matrices. The motivation comes from applications where the matrix in question has distinguished block structure, which can be exploited to obtain useful information. An example arising from ecological modeling illustrates the benefits of the presented approach.