BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-69-122
       ENTRY:: November 27, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Heuristic analysis of numerical variants of the Gram-Schmidt
               orthonormalization process
        TYPE:: Technical Report
      AUTHOR:: Mitchell, William C.
      AUTHOR:: McCraith, Douglas L.
        DATE:: February 1969
       PAGES:: 24
    ABSTRACT:: The Gram-Schmidt orthonormalization process is a fundamental
               formula of analysis which is notoriously unstable
               computationally. This report provides a heuristic analysis of
               the process, which shows why the method is unstable. Formulas
               are derived which describe the propagation of round-off error
               through the process. These formulas are supported by
               numerical experiments. These formulas are then applied to a
               computational variant of a basic method proposed by John R.
               Rice, and this method is shown to offer significant
               improvement over the basic algorithm. This finding is also
               supported by numerical experiment.

               The formulas for the error propagation are then used to
               produce a linear corrector for the basic Gram-Schmidt
               process, which shows significant improvement over both
               previous methods, but at the cost of slightly more
               computations.
       NOTES:: [Adminitrivia V1/Prg/19951127]
         END:: STAN//CS-TR-69-122