Infinity Norm Bounds for the Inverse of $GSDD_k$ Matrices with Applications

Source abstract

In this paper, we investigate a new subclass of nonsingular $H$-matrices called $GSDD_k$ matrices. The relationships between $GSDD_k$ matrices and other subclasses of nonsingular $H$-matrices are analyzed. Moreover, the infinity norm bounds for the inverse of $GSDD_k$ matrices are obtained. Based on the relationship between strictly diagonally dominant ($SDD$) matrices and $GSDD_k$ matrices, infinity norm bounds for the inverse of $SDD$ matrices are also derived, which improve some existing bounds. Furthermore, error bounds of linear complementarity problems involving $GSDD_k$ matrices and $SDD$ matrices are given. Numerical examples demonstrate the effectiveness of the new results.