The rank revealing QR factorization of a rectangular matrix can sometimes be used as a reliable and efficient computational alternative to the singular value decomposition for problems that involve rank determination. This is illustrated by showing how the rank revealing QR factorization can be used to compute solutions to rank deficient least squares problems, to perform subset selection, to compute matrix approximations of given rank, and to solve total least squares problems.
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Chan et al. (1992) studied this question.
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