The Update Step in Linear Programming using Modified Givens Transformations.

摘要

An efficient and numerically stable method is presented for the problem of updating an orthogonal decomposition of a matrix of coulmn (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 application of the Givens transformation in modified (more efficient) form. Some suggested computational tests for determining signs of various controlling parameters in the revised simplex algorithm are also given. (Author)