NAG Fortran Library Routine Document F11DNF

F11DNF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose F11DNF computes an incomplete LU factorization of a complex sparse non-Hermitian matrix, represented in coordinate storage format. This factorization may be used as a preconditioner in combination with F11DQF or F11BSF. real DTOL complex A(LA) CHARACTER * 1 PSTRAT, MILU 3 Description This routine computes an incomplete LU factorization (Meijerink and Van der Vorst (1977), Meijerink and Van der Vorst (1981)) of a complex sparse non-Hermitian n by n matrix A. The factorization is intended primarily for use as a preconditioner with one of the iterative solvers F11DQF or F11BSF. The decomposition is written in the form A ¼ M þ R; where M ¼ P LDUQ and L is lower triangular with unit diagonal elements, D is diagonal, U is upper triangular with unit diagonals, P and Q are permutation matrices, and R is a remainder matrix. The amount of fill-in occurring in the factorization can vary from zero to complete fill, and can be controlled by specifying either the maximum level of fill LFILL, or the drop tolerance DTOL. The argument PSTRAT defines the pivoting strategy to be used. The options currently available are no pivoting, user-defined pivoting, partial pivoting by columns for stability, and complete pivoting by rows for sparsity and by columns for stability. The factorization may optionally be modified to preserve the row-sums of the original matrix. The sparse matrix A is represented in coordinate storage (CS) format (see Section 2.1.1 of the F11 Chapter Introduction). The array A stores all the non-zero elements of the matrix A, while arrays IROW and ICOL store the corresponding row and column indices respectively. Multiple non-zero elements may not be specified for the same row and column index.