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.
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Charles Van Loan (1985) studied this question.
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