A New Product Form of the Inverse

Many algorithms of solving linear programs are based on the revised simplex method. The product form of the inverse is used to inverse the base in the revised simplex method.We present in this paper an inversion of matrix which complexity is quadratic. This method is more efficient than the product form of the inverse. We tested the revised simplex method and the algorithm proposed about 55 linear problems. The densities of the LPs are 10%, 5 % and 2.5%. they are randomly generated