The algebraic eigenvalue problem
The algebraic eigenvalue problem
Linear programming 1: introduction
Linear programming 1: introduction
ACM Transactions on Mathematical Software (TOMS)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
Pracniques: construction of nonlinear programming test problems
Communications of the ACM
Large-scale linear programming using the Cholesky factorization.
Large-scale linear programming using the Cholesky factorization.
Structured programming
| Hi-index | 48.22 |
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 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.