The Elimination form of the Inverse and its Application to Linear Programming - Markowitz, Harry M. (Management Science, 1957)
It is common for matrices in industrial applications of linear programming to have a large proportion of zero coefficients. While every item (raw material, intermediate material, end item, equipment item) in, say, a petroleum refinery may be indirectly related to every other, any particular process uses few of these. Thus the matrix describing petroleum technology has a small percentage of non-zeros. If spacial or temporal distinctions are introduced into the model the percentage of non-zeros generally falls further. The present paper discusses a form of inverse which is especially convenient to obtain and use for matrices with a high percentage of zeros. The application of this form of inverse in linear programming is also discussed.