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 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)
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)
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)
We describe the design of a new code for the direct solution of sparse unsymmetric linear systems of equations. The new code utilizes a novel restructuring of the symbolic and numerical phases, which increases speed and saves storage without sacrifice of numerical stability. Other features include switching to full-matrix processing in all phases of the… (More)
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)
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.
For a sparse symmetric matrix, there has been much attention given to algorithms for reducing the bandwidth. As far as we can see, little has been done for the unsymmetric matrix A, which has distinct lower and upper bandwidths l and u. When Gaussian elmination with row interchanges is applied, the lower bandwidth is unaltered while the upper bandwidth… (More)