Low-density incomplete LDLT factorizations

A particular class of incomplete factorizations is proposed as preconditioners for the linear system Ax = b where A is a symmetric, large and sparse matrix. The ILDL ^T< (p) factorization (p = 1,2,3, …) determines the density of the lower triangular matrix L selecting the p largest off-diagonal entries of each column during the Gaussian elimination process. This selection may be computationally expensive, but the effectiveness of the preconditioner allows us to choose very low-density factors to reduce both work time and storage requirements. This incomplete factorization can be performed reliably on H-matrices. When A is a positive definite matrix, but not an H-matrix, one can perform an incomplete factorization if positive off-diagonal entries are removed or reduced and diagonally compensated. Numerical results for a variety of problems and comparisons with other incomplete factorizations are presented. Received: August 2002 / Accepted: December 2002 RID="*" ID="*"This work was supported by the Spanish grant BFM 2001-2641.