05988498

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05988498 Pe\~na, Juan Manuel Diagonal dominance, Schur complements and some classes of $H$-matrices and $P$-matrices. Adv. Comput. Math. 35, No. 2-4, 357-373 (2011). 2011 Springer, Dordrecht EN $H$-matrices $P$-matrices diagonal dominance by row pivoting Schur complement algorithm complexity

doi:10.1007/s10444-010-9160-5

$SDD_1$-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. Martin Rei\ss el (Aachen)