Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices

Abstract

In this paper, a new proof that $ SDD_1 $ matrices is a subclass of $ H $-matrices is presented, and some properties of $ SDD_1 $ matrices are obtained. Based on the new proof, some upper bounds of the infinity norm of inverse of $ SDD_1 $ matrices and $ SDD $ matrices are given. Moreover, we show that these new bounds of $ SDD $ matrices are better than the well-known Varah bound for $ SDD $ matrices in some cases. In addition, some numerical examples are given to illustrate the corresponding results.

Keywords

• sdd₁ matrices
• sdd matrices
• upper bound
• positive diagonal matrix
• infinity norm