MA57---a code for the solution of sparse symmetric definite and indefinite systems

We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of the implementation details and emphasize the novel features of MA57. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom.