Local algorithms for obtaining a pivot ordering for sparse symmetric coefficient matrices are reviewed together with their mathematical background and appropriate data structures. Recently proposed heuristics as well as improvements to them are discussed, and their performance, mainly in terms of the resulting number of factorization operations, is compared with that of the Minimum Degree and t...

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to sequential execution. We present a sample MPI implementation of a program computing the rank of a sparse integer matrix using the proposed algorithm. Some prelim...

We consider the solution of ill-conditioned symmetric and positive definite large sparse linear systems of equations. These arise, for instance, when using some symmetrizable preconditioning technique for solving a general (possibly unsymmetric) ill-conditioned linear system, or in domain decomposition of a numerically difficult elliptic problem. We are also concerned with the consecutive solut...

We report on the design and development of a parallel frontal code HSL–MP43 for the numerical solution of the large sparse highly unsymmetric linear systems of equations that arise in industrial-scale chemical process engineering. HSL–MP43 has been developed for the mathematical software library HSL 2000 (http://www.cse.clrc.ac.uk/Activity/HSL). The main design goals for HSL–MP43 were: probabil...

For unsymmetric block-tridiagonal systems of linear equations arising from the discretization of partial differential equations, a composite preconditioner is proposed and tested. It combines a classical ILU0 factorization for high frequencies with a tangential filtering preconditioner. The choice of the filtering vector is important: the test-vector is the Ritz eigenvector corresponding to the...

We report on the design and development of a parallel frontal code for the numerical solution of the large sparse highly unsymmetric linear systems of equations that arise in industrial-scale chemical process engineering. The code has been developed as routine HSL MP43 for the mathematical software library HSL 2000 The main design goals for HSL MP43 were: portability, ease of use, eeciency, and...