BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-70-162
       ENTRY:: November 06, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Numerical techniques in mathematical programming
        TYPE:: Technical Report
      AUTHOR:: Bartels, Richard H.
      AUTHOR:: Golub, Gene H.
      AUTHOR:: Saunders, Michael A.
        DATE:: May 1970
       PAGES:: 74
    ABSTRACT:: The application of numerically stable matrix decompositions
               to minimization problems involving linear constraints is
               discussed and shown to be feasible without undue loss of
               efficiency.

               Part A describes computation and updating of the product-form
               of the LU decomposition of a matrix and shows it can be
               applied to solving linear systems at least as efficiently as
               standard techniques using the product-form of the inverse.

               Part B discusses orthogonalization via Householder
               transformations, with applications to least squares and
               quadratic programming algorithms based on the principal
               pivoting method of Cottle and Dantzig.

               Part C applies the singular value decomposition to the
               nonlinear least squares problem and discusses related
               eigenvalue problems.
       NOTES:: [Adminitrivia V1/Prg/19951106]
         END:: STAN//CS-TR-70-162