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 rowsums of the original matrix. The sparse matrix A is represented in coordinate stora...

We consider the block LDL factorizations for symmetric indefinite matrices in the form LBL , where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving linear systems has been well-studied in the literature. In this paper we give a condition under which the LBL factorization will r...

We show that there are simplex pivoting rules for which it is PSPACE-complete to tell if a particular basis will appear on the algorithm’s path. Such rules cannot be the basis of a strongly polynomial algorithm, unless P = PSPACE. We conjecture that the same can be shown for most known variants of the simplex method. However, we also point out that Dantzig’s shadow vertex algorithm has a polyno...

This paper gives sensitivity analyses by two approaches for L and U in the factor-ization A = LU for general perturbations in A which are suuciently small in norm. By the matrix-vector equation approach, we derive the condition numbers for the L and U factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting aaect th...

Recent work by Sweet and Brent on the fast factorization of Cauchy-like matrices through a fast version of Gaussian elimination with partial pivoting has uncovered a potential stability problem which is not present in ordinary Gaussian elimination: excessive growth in the generators used to represent the matrix and its Schur complements can lead to large errors. A natural way to x this problem ...

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 w...