Infinity norm upper bounds for the inverse of $ {SDD_k} $ matrices

Abstract

In this paper, we introduce a new subclass of $ H $-matrices called $ {SDD_k} $ matrices, which contains $ {SDD} $ matrices and $ {SDD_1} $ matrices as special cases, and present some properties of $ {SDD_k} $ matrices. Based on these properties, we also provide new infinity norm bounds for the inverse of $ {SDD} $ matrices and $ {SDD_k} $ matrices. It is proved that these new bounds are better than some existing results in some cases. Numerical examples demonstrate the effectiveness of the obtained results.

Keywords

• $ {sdd_k} $ matrices
• $ {sdd} $ matrices
• $ {sdd_1} $ matrices
• infinity norm
• upper bound