Extended \(SDD_1^{\dag } \) matrices and error bounds for linear complementarity problems

In this paper, we introduce a new subclass of H-matrices named extended \(SDD_1^{\dag } \) $SD{D}_1^{†}$ (for shortly, \(ESDD_1^{\dag } \) $ESD{D}_1^{†}$ ) matrices, discuss the relationships among \(ESDD_1^{\dag } \) $ESD{D}_1^{†}$ matrices and other subclasses of H-matrices. Based on the properties of \(ESDD_1^{\dag } \) $ESD{D}_1^{†}$ matrices, infinity norm upper bounds for the inverse of \(ESDD_1^{\dag } \) $ESD{D}_1^{†}$ matrices are presented. As an application, error bound for linear complementarity problems of \(ESDD_1^{\dag } \) $ESD{D}_1^{†}$ matrices is provided. Numerical examples show that the obtained results are better than some existing bounds.