Infinity norm bounds for the inverse of generalized \({SDD_2}\) matrices with applications

A new subclass of H-matrices named generalized \(SDD_2\) $SD{D}_2$ (for shortly, \(GSDD_2\) $GSD{D}_2$ ) matrices is introduced and some properties of \(GSDD_2\) $GSD{D}_2$ matrices are presented. The relationship between \(GSDD_2\) $GSD{D}_2$ matrices and other subclasses of H-matrices is studied. Moreover, the infinity norm bounds for the inverse of \(GSDD_2\) $GSD{D}_2$ matrices are provided. Using the proposed infinity norm bounds, error bounds of the linear complementarity problems for \(GSDD_2\) $GSD{D}_2$ matrices are given, which improve some existing results. Numerical examples are given to illustrate the validity of new results.