A New Subclass of H-Matrices and Their Schur Complement

Nekrasov matrices, as a subclass of $$H$$ -matrices, exhibit unique functionalities and hold significant importance in diverse fields. These matrices are characterized by their distinctive structure, which endows them with numerous remarkable properties. Our paper extends the study of Nekrasov matrices by introducing a new subclass of $$H$$ -matrices, termed $$DN$$ -matrices, and explores their properties, particularly focusing on the Schur complement.