BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-72-301
       ENTRY:: October 16, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Product form of the Cholesky factorization for large-scale
               linear programming.
        TYPE:: Technical Report
      AUTHOR:: Saunders, Michael A.
        DATE:: August 1972
       PAGES:: 41
    ABSTRACT:: A variation of Gill and Murray's version of the revised
               simplex algorithm is proposed, using the Cholesky
               factorization ${BB}^T = {LDL}^T$ where B is the usual basis,
               D is diagonal and L is unit lower triangular. It is shown
               that during change of basis L may be updated in product form.
               As with standard methods using the product form of inverse,
               this allows use of sequential storage devices for
               accumulating updates to L. In addition the favorable
               numerical properties of Gill and Murray's algorithm are
               retained.

               Cloase attention is given to efficient out-of-core
               implementation. In the case of large-scale block-angular
               problems, the updates to L will remain very sparse for all
               iterations.
       NOTES:: [Adminitrivia V1/Prg/19951016]
         END:: STAN//CS-TR-72-301