Development of software for solving systems of linear equations

Abstract: "This report discusses the design and implementation of software for solving systems of sparse linear equations. The motivation for this work came from the needs of the ASCEND (Piela, 1989) computer environment for building and solving complex mathematical models. The original intent was to use an existing software package such as MA28 (from the United Kingdom Atomic Energy Authority, Harwell) (Duff, 1977); however, an initial survey convinced us that a package to suit our requirements for an extremely flexible research tool did not exist.We were looking for software that had been written in a modular fashion, allowing us to change all aspects of the solving process such as matrix representation, and solving algorithm. In response to these requirements, we created our own software package which is described in this report. The report is divided into four sections, the first of which describes in detail the software structure and implementation of the solver. The second section describes the methods used for testing both the correctness and efficiencyof the solver. The third section discusses the development of the solving algorithm, and in the fourth section the solver is compared with two other packages: MA28, and a solver developed by Amoco (Cummings, 1985)."