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

by: Charles Van Loan
SIAM Journal on Numerical Analysis, Vol. 22, No. 5. (1985), pp. 851-864.

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The generalized singular value decomposition is used to analyze the problem of minimizing | Ax - b |<sub>2</sub> 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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