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ACM Transactions on Mathematical Software (TOMS)
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ACM Transactions on Mathematical Software (TOMS)
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This paper is concerned with least squares problems when the least squares matrix A is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain conditions when A has numerical rank r there is a distinguished r dimensional subspace of the column space of A that is insensitive to how it is approximated by r independent columns of A. The consequences of this fact for the least squares problem are examined. Algorithms are described for approximating the stable part of the column space of A.