Diagonal dominance, Schur complements and some classes of \(H\)-matrices and \(P\)-matrices (Q652574)

\(SDD_1\)-matrices are introduced as a special class of \(H\)-matrices which generalize strict diagonal dominance by rows. One result of the theoretical investigations is an algorithm of complexity \(O(n^2)\) for checking whether a square matrix belongs to the class \(SDD_1\) or not. The class of \(SDD_1\)-matrices is closed with respect to symmetric pivoting, but not with respect to Schur complements. To overcome this difficulty, symmetric pivoting strategies are presented which result in \(SDD_1\) Schur complements. Finally, \(SDD_1\)-matrices are used to find a new class of \(P\)-matrices.