On the Method of Weighting for Equality-Constrained Least-Squares Problems

The generalized singular value decomposition is used to analyze the problem of minimizing $||Ax b||_{2}$ subject to the constraint Bx = d. A byproduct of the analysis is a new iterative procedure that can be used to improve an approximate solution obtained via the method of weights. All that is required to implement the procedure is a single QR factorization. These developments turn out to be of interest when A and B are sparse and for the case when systolic architectures are used to carry out the computations.