Balanced Incomplete Factorization

Improved Balanced Incomplete Factorization

In this paper we improve the BIF algorithm which computes simultaneously the LU factors (direct factors) of a given matrix, and their inverses (inverse factors). This algorithm was introduced in [R. Bru, J. Maŕın, J. Mas and M. Tůma, SIAM J. Sci. Comput., 30 (2008), pp. 2302– 2318]. The improvements are based on a deeper understanding of the Inverse Sherman-Morrison (ISM) decomposition and they...

BIF: Balanced Incomplete Factorization

Incomplete factorizations represent a class of algebraic preconditioners important from both theoretical and practical points of view. While state-of-the-art preconditioners of this kind can be very useful, very large problems, arising, e.g., from discretizations of complicated operators on unstructured grids typically, still may require more robust preconditioners. High-quality incomplete fact...

Balanced Incomplete Factorization

In this paper we present a new incomplete factorization of a square matrix into triangular factors in which we get standard LU or LDL T factors (direct factors) and their inverses (inverse factors) at the same time. Algorithmically, we derive this method from the approach based on the Sherman-Morrison formula [18]. In contrast to the RIF algorithm [11], the direct and inverse factors here direc...

Splitting balanced incomplete block designs

Beautifully Ordered Balanced Incomplete Block Designs

Beautifully Ordered Balanced Incomplete Block Designs, BOBIBD(v, k, λ, k1, λ1), are defined and the proof is given to show that necessary conditions are sufficient for the existence of BOBIBD with block size k=3 and k1=2 and for k=4 and k1=2 except possibly for eleven exceptions. Existence of BOBIBDs with block size k=4 and k1=3 is demonstrated for all but one infinite family and the non-existe...