Basis inverse of large-scale and sparse linear programming problems

This paper gives a brief survey on the methods for computing and updating the basis inverse of large-scale and sparse linear programming problems. In addition, it presents a new method for pivot searching which takes the numerical effects of the previous transformations also into account. Tests were made of the different methods on numerically unstable bases arising in practical problems. The present expectation on the better numerical behaviour of the new pivot searching has been justified by the computational experiments.