Rank Revealing QR-Factorizations.
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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An algorithm is presented for computing a column permutation Pi and a QR-factorization APi QR of an m by n m or n matrix A such that a possible rank deficiency of A will be revealed in the triangular factor R having a small lower right block. For low rank deficient matrices, the algorithm is guaranteed to reveal the rank of A and the cost is only slightly more than the cost of one regular QR-factorization. A posteriori upper and lower bounds on the singular values of A are derived and can be used to infer the numerical rank of A. Keywords QR-Factorization Rank deficient matrices Least squares computation Subset selection Rank Singular values.
- Statistics and Probability