A Fast LU Decomposition Algorithm for the Sparse Revised Simplex Method

Many algorithms reduce fill-ins in LU decomposition by rearranging columns and rows of the sparse matrix. We take a different approach for the LU decomposition in the revised simplex algorithm. The basis matrix in this algorithm is extremely sparse and there are many column and row singletons. We propose a new algorithm to rearrange the column and row singletons iteratively. This algorithm reduces the size of the submatrix to be factorized to minimal. It reduces fill-ins and computation time drastically. This algorithm has been tested on many realistic data from netlib, ranging from small-scale to large-scale.