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Asymptotic expressions are derived for the singular value decompositon of a matrix some of whose columns approach zero. Expressions are also derived for the QR factorization of a matrix some of whose rows approach zero. The expressions give insight into the method of weights for approximating the solutions of constrained least squares problems.doi:10.2307/2008289 fatcat:ljxen3mmhvgv3f7yc32ygahylu