Improved Balanced Incomplete Factorization

0351682 - ÚI 2011 RIV US eng J - Journal Article
Bru, R. - Marín, J. - Mas, J. - Tůma, Miroslav
Improved Balanced Incomplete Factorization.
SIAM Journal on Matrix Analysis and Applications. Roč. 31, č. 5 (2010), s. 2431-2452. ISSN 0895-4798. E-ISSN 1095-7162
R&D Projects: GA AV ČR IAA100300802
Grant - others:GA AV ČR(CZ) M100300902
Institutional research plan: CEZ:AV0Z10300504
Source of funding: I
Keywords : preconditioned iterative methods * sparse matrices * incomplete decompositions * approximate inverses * Sherman-Morrison formula * nonsymmetric matrices
Subject RIV: BA - General Mathematics
Impact factor: 1.725, year: 2010

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. Marín, 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 provide a new insight into the BIF decomposition. In particular, it is shown that a slight algorithmic reformulation of the basic algorithm implies that the direct and inverse factors numerically influence each other even without any dropping for incompleteness. Algorithmically, the nonsymmetric version of the improved BIF algorithm is formulated. Numerical experiments show very high robustness of the incomplete implementation of the algorithm used for preconditioning nonsymmetric linear systems.
Permanent Link: http://hdl.handle.net/11104/0191385