We extend the frontal method for solving linear systems of equations by permitting more than one front to occur at the same time. This enables us to develop code for general symmetric systems. We discuss the orgamzation and implementatmn of a multifrontal code which uses the minimum-degree ordering and indicate how we can solve indefinite systems in a… (More)
We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its… (More)
We describe the design of a new code for the solution of sparse indefinite symmetric linear systems of equations. The principal difference between this new code and earlier work lies in the exploitation of the additional sparsity available when the matrix has a significant number of zero diagonal entries. Other new features have been included to enhance the… (More)
In the hght of practical experience with HarweU subroutine MA18 for solwng sparse sets of hnear equations by Gaussian elunmation and the growth of knowledge in data structure mampulatmn, we make some comments on techmques which can be usefully employed in such a code Most of these suggestmns have been incorporated m the new HarweU sparse matrix package MA28.
An implementation of Tarj an's algorithm for symmetrically permuting a given matrix to block tmangular form is described. The discussion includes a flowchart of the algorithm, a complexity analysis, and a comparison with the earlier widely used algorithm of Sargent and Westerberg. T~ming results are presented from several experiments using the code… (More)
Direct methods for solving large sparse linear systems of equations are popular because of their generality and robustness. Their main weakness is that the memory they require usually increases rapidly with problem size. We discuss the design and development of the first release of a new symmetric direct solver that aims to circumvent this limitation by… (More)
Given the column numbers of the nonzeros in each row of a sparse matrix, this subroutine finds a symmetric permutation that makes the matrix block lower triangular. I t can also be interpreted as accepting the row numbers of the non-zeros in each column and symmetrically permuting to block upper triangular form. If the user submits a matrix with zeros on… (More)
This article presents the first extended set of results from EliAD, a source-transformation implementation of the vertex-elimination Automatic Differentiation approach to calculating the Jacobians of functions defined by Fortran code (Griewank and Reese, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, 1991, pp. 126--135).… (More)