Abstract
This paper discusses sparse matrix kernels of simplex-based linear programming software. State-of-the-art implementations of the simplex method maintain an LU factorization of the basis matrix which is updated at each iteration. The LU factorization is used to solve two sparse sets of linear equations at each iteration. We present new implementation techniques for a modified Forrest-Tomlin LU update which reduce the time complexity of the update and the solution of the associated sparse linear systems. We present numerical results on Netlib and other real-life LP models.
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