Partition−Nekrasov type matrices: A new subclass of nonsingular H−matrices and applications

Abstract

Nonsingular H−matrices have proven to be a source of many interesting results in different research areas in numerical linear algebra and also in applications in economy, engineering, ecology. In this paper, a new criteria for identifying some special H−matrices is presented. It is based on attributing different partition of the index set to each row of the matrix in consideration and testing inequalities that are associated to these partitions and involve recursively defined Nekrasov row sums. The new subclass of H−matrices introduced in this way is then analyzed with respect to its relation to well-known matrix classes. We used our new condition to estimate norm of the inverse matrix and errors in linear complementarity problems that involve matrices of this type.