OPTIMQR is a software package that can generate a fast solver for sparse linear systems of equations. The generated solver uses the QR factorization.
The systems we work with are sparse and their sparsity patterns are constant. The non-zero values can vary, but the structure must be invariant.
QR factorization is more expensive in terms of FLOPS, than many other factorizations. But it does not require re-ordering of rows, in order to maintain numerical stability. If we can just fix the rows and columns in our system once and for all, we can solve any system obeying the fixed structure for which the solver was generated.
The OPTIMQR package allows a user to generate an efficient solver for some given system structure. The structure is given in an input file to the optimizer program, and the output from that can be used to generate a FORTRAN-77 subroutine, using the code generator program.
I recommend that users of this package familiarize themselves with the workings of OPTIMQR by skimming [OptimQR].