Subdirect Sums of $ GSD{D_1} $ matrices

Abstract

The class of generalized $ SD{D_1} \; \left({GSD{D_1}} \right) $ matrices is a new subclass of $ H $-matrices. In this paper, we focus on the subdirect sum of $ GSD{D_1} $ matrices, and some sufficient conditions to ensure that the subdirect sum of $ GSD{D_1} $ matrices with strictly diagonally dominant $ \left({SDD} \right) $ matrices is in the class of $ GSD{D_1} $ matrices are given. Moreover, corresponding examples are given to illustrate our results.

Keywords

• subdirect sum
• $ h $-matrices
• $ gsd{d_1} $ matrices
• strictly diagonally dominant matrices
• sufficient conditions