On the Method of Weighting for Equality-Constrained Least-Squares Problems
Charles F. Van Loan · SIAM Journal on Numerical Analysis · 1985
The generalized singular value decomposition is used to analyze the problem of minimizing $\| {Ax - b} \|_2 $ subject to the constraint $Bx = d$. A by-product 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.