Block LU factorization is stable for block matrices whose inverses are block diagonally dominant

Let A M_n (C) and let the inverse matrix B = A^–1 be block diagonally dominant by rows (columns) w.r.t. an m × m block partitioning and a matrix norm. We show that A possesses a block LU factorization w.r.t. the same block partitioning, and the growth factor for A in this factorization is bounded above by 1 + , where = max _{1im i} and _i, 0 _i 1, are the row (column) block dominance factors of B. Further, the off-diagonal blocks of A (and of its block Schur complements) satisfy the inequalities Bibliography: 4 titles._________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 296, 2003, pp. 15–26.