Parallel Solution Alternatives for Sparse Triangular Systems in Interior Point Methods

Abstract

The repeated solution of large symmetric sets of linear equations, which constitutes the major computational effort in interior point algorithms, requires efficient implementations of triangular system solvers. In this study, we present some parallel solution alternatives for these sparse triangular linear systems. Several forward and backward solution algorithms are tested, and a scalable buffered backward solution algorithm, which outperforms the other back substitution algorithms, is developed. Performance results are presented from a number of real application problems from the NETLIB suite.