3138	 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 - 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. Linear programming numerical linear algebra modified Givens transformations linear programming test cases
