Infinity Norm Bounds for the Inverse of \(GSDD_k\) Matrices with Applications

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.