A Projection Method for the Solution of Rectangular Systems
Jesús Cardenal, I S Duff, J M Jimenez · 1996
We present a general method for the linear least-squares solution of overdetermined and underdetermined systems. The method is particularly efficient when the coefficient matrix is quasi-square, that is when the number of rows and number of columns is almost the same. The numerical methods proposed in the literature for linear least-squares problems and minimum-norm solutions do not generally take account of this special characteristic. The proposed method is based on an LU factorization of the original quasi-square matrix A, assuming that A has full rank. In the overdetermined case, the LU factors are used to compute a basis for the null space of A T . The right-hand side vector b is then projected onto this subspace and the least-squares solution is obtained from the solution of this reduced problem. In the case of underdetermined systems, the desired solution is again obtained through the solution of a reduced system. The use of this method may lead to important savings in comput...