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 LDLT 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 directly influence each other throughout the computation. Consequently, the algorithm to compute the approximate factors may mutually balance dropping in the factors and control their conditioning in this way. For the symmetric positive definite case, we derive the theory and present an algorithm for computing the incomplete LDLT factorization, and discuss experimental results. We call this new approximate LDLT factorization the Balanced Incomplete Factorization (BIF). Our experimental results confirm that this factorization is very robust and may be useful in solving difficult ill-conditioned problems...

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Rafael Bru, José Marín, José Mas, Miroslav Tuma
• Keywords: Incomplete Factorization, Inverse Factors, LDLT Factorization, SIAMSC 2008