A Mathematical Programming Updating Method Using Modified
Givens Transformations and Applied to LP Problems

An efficient and numerically stable method is presented for the problem of
updating an orthogonal decomposition of a matrix of column (or row) vectors.
The fundamental idea is to add a column (or row) analogous
to adding an additional row of data in a linear least squares problem.
A column (or row) is dropped by a formal scaling with the
imaginary unit,  -1, followed by least squares addition of the column
(or row).  The elimination process for the procedure is successive
ssive application of the Givens transformation in modified (more efficient)
form.  These ideas are illustrated with an implementation
of the revised simplex method.  The algorithm is a general purpose
one that does not account for any particular structure or sparsity
in the equations.  Some suggested computational tests for determining
signs of various controlling parameters in the revised simplex
algorithm are mentioned.  A simple means of constructing
test cases and some sample computing times are presented. 

CACM April, 1979

Hanson, R.
Wisniewski, J.

Linear programming, numerical linear algebra, modified Givens transformations,
linear programming test cases

5 5.4 5.41 5.1 5.14

CA790404 DH May 21, 1979  2:06 PM

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