Low-density incomplete \(LDL^T\) factorizations (Q2568738)

The authors propose new drop tolerance incomplete factorizations for symmetric matrices. Negative fill-in produces Cholesky square-free \(LDL^T\) incomplete factorization where the factorization density can be chosen to be smaller than that of the given matrix. Two algorithms compute an incomplete \(LDL^T(p)\) factorization where \(p\) is the maximum number of non-zero off-diagonal entries per column in the computed factor \(L\). In the first algorithm, the dropping of entries is performed at each pivot column to reduce fill-in and computations on the active submatrix updating. In the second algorithm, the dropping is performed at every column of the matrix \(L\) such that, in every step, dropping is applied to a maximum of \(2p\) non-zero entries and the storage is limided to \((p+1)n\) non zero-entries in the whole process. Numerical tests are performed for several matrices.