Bounds for elements of LU factorizations of sparse matrices and their application to incomplete factorization methods (Q1974749)

The author considers a difference approximation of a model elliptic boundary value problem. The bounds for elements of LU factorizations are obtained for matrices associated with corresponding sets of linear algebraic equations, that result from the discretization of this elliptic boundary value problem. For the case of block factorizations, the bounds obtained in this paper are two-sided and cannot be improved upon asymptotically. These bounds are substantially more exact than were known earlier.