Perturbed matrix inversion with application to LP simplex method

Computation of the inverse of a perturbed matrix (A + D)−1 appears within various areas of research and applications. Of particular importance is the sparse simplex, where A is the basis matrix. In this paper a procedure for the computing of the inverse matrix (A + D)−1 is presented and discussed, where A∈Rn×nA∈Rn×n is a given non-singular matrix, A−1 is already calculated, and A + D is a perturbed matrix of A by D, where D is sparse. The non-singularity requirement for D is removed.