Infinity norm bounds for the inverse of Quasi-\(SDD_k\) matrices with applications

In this paper, we propose a new subclass of H-matrices named Quasi- \(SDD_k\) $SD{D}_k$ (for shortly, \(QSDD_k\) $QSD{D}_k$ ) matrices, present some properties of \(QSDD_k\) $QSD{D}_k$ matrices, and discuss the relationship among \(QSDD_k\) $QSD{D}_k$ matrices and other subclasses of H-matrices. Moreover, the infinity norm bounds for the inverse of \(QSDD_k\) $QSD{D}_k$ matrices and error bounds for the linear complementarity problems of \(QSDD_k\) $QSD{D}_k$ matrices are given, which improve some existing results. Numerical examples are given to illustrate the validity of new results.